Norbert Sauer

Professor Emeritus

Department of Mathematics and Statistics

PhD

University of Vienna, 1966

Contact information

Phone

Office: 403.220.6309

Location

Office : MS526

Research and teaching

Research areas

  • Set theory
  • Universal algebra
  • Graph theory
  • Theory of homogeneous structures
  • Partially ordered sets
  • Relational structures
  • Ramsey theory

Publications

Book

  • Sauer, Norbert. Coloring finite substructures of countable structures 11. J\'anos Bolyai Math. Soc., 2002. 525-553. Print.
  • Wang, Hong and Sauer, Norbert. The chromatic number of the two-packing of a forest 14. Springer, 1997. 99-120. Print.
  • Imrich, Wilfried, Sauer, Norbert and Woess, Wolfgang. The average size of nonsingular sets in a graph 411. Kluwer Acad. Publ., 1993. 199-205. Print.
  • Sauer, Norbert. Vertex partition problems , J\'anos Bolyai Math. Soc., 1993. 361-377. Print.
  • Sauer, Norbert and Zhu, X.. Graphs which do not embed a given graph and the {R}amsey property 60. North-Holland, 1992. 631-636. Print.
  • Sauer, Norbert and El-Zahar, M.. Partition theorems for graphs respecting the chromatic number 301. Kluwer Acad. Publ., 1990. 237-242. Print.
  • Sauer, Norbert and Stone, Mike. Preemptive scheduling Kluwer Acad. Publ., 1989. 307-323. Print.
  • Sauer, Norbert and Stone, Mike. A characterization of extendible lattices H\"older-Pichler-Tempsky, 1988. 243-246. Print.
  • Sauer, Norbert and Stone, Mike. Indigenous relations in categories of sets H\"older-Pichler-Tempsky, 1987. 313-320. Print.
  • Sauer, Norbert and Stone, Mike. Monoids and their local closures 43. North-Holland, 1986. 455-467. Print.
  • Sauer, Norbert and Stone, Mike. Extendible lattices H\"older-Pichler-Tempsky, 1985. 331-334. Print.
  • Koh, K. M. and Sauer, Norbert. Concentric subgraphs, closed subsets and dense graphs 1073. Springer, 1984. 100-118. Print.
  • Sauer, Norbert, Stone, Mike and Weedmark, R. H.. Every finite algebra with congruence lattice {$M\sb{7}$} has principal congruences 1004. Springer, 1983. 273-292. Print.
  • Sauer, Norbert and Stone, Mike. A {G}alois correspondence between algebras and endomorphisms 29. North-Holland, 1982. 691-695. Print.
  • Sauer, Norbert. The largest number of edges of a graph such that not more than {$g$}\ intersect in a point or more than {$n$} are independent Academic Press, 1971. 253-257. Print.
  • Sauer, Norbert. On the factorization of {$n$}-graphs North-Holland, 1970. 981-995. Print.
  • Kuich, W. and Sauer, Norbert. On the existence of certain minimal regular {$n$}-systems with given girth Academic Press, 1969. 93-101. Print.

Conference proceedings

  • Sauer, Norbert. Age and weak indivisibility 2008.

Forthcoming

  • Nguyen Van Thé, Lionel and Sauer, Norbert. The Urysohn sphere is oscillation stable (updated version). 2007.

Journal article

  • Laflamme, Claude, Pouzet, Maurice and Sauer, Norbert. "Invariant subsets of scattered trees and the tree alternative property of Bonato and Tardif". Abhandlungen Math. Sem. Univ. Hamburg Volume in memory of Rudolf Halin. (2017): 1-40. Print.
  • Laflamme, Claude, Sauer, Norbert and Dobrinen, Natasha. "Rainbow Ramsey simple structures". Discrete Mathematics 339.11 (2016): 2848-2855. Print.
  • Laflamme, Claude, Sauer, Norbert, Pouzet, Maurice and Zaguia, Imed. "Pairs of orthogonal countable ordinals". Discrete Mathematics 335. (2015): 35-44. Print.
  • Sauer, Norbert. "Age and weak indivisibility". European Journal of Combinatorics, (2015). Print.
  • Sauer, Norbert, P. Komjath and J. Larson. "The Quasiorder of Graphs on an Ordinal". Discrete Mathematics 311. (2015): 151-146. Print.
  • Sauer, Norbert. "Distance sets of Urysohn metric spaces". Canadian Journal of Mathematics 65.1 (2013): 220-240. Print.
  • Sauer, Norbert. "Oscillation of Urysohn Type Spaces". Asymptotic Geometric Analyis, Fields Institute Communications 68. (2013): 247-270. Print.
  • Sauer, Norbert. "Vertex partitions of metric spaces with finite distance sets". Discrete Mathematics 312.1 (2012): 119-128. Print.
  • Sauer, Norbert. "On the General Coloring Problem". Lecture Notes in Computer Science 6570. (2011): 116-126. Print.
  • Sauer, Norbert and I. Zaguia. "The order of the rationals has an Orthogonal Order with the Same Order Type". Order 28. (2011): 377-385. Print.
  • Laflamme, Claude, Nguyen Van Thé, Lionel and Sauer, Norbert. "Distinguishing Number of Countable Homogeneous Relational Structures". Electronic Journal of Combinatorics 16(1). (2010). Print.
  • Laflamme, Claude, Nguyen Van Thé, Lionel and Sauer, Norbert. "Partition properties of the dense local order and a colored version of Milliken's theorem.". Combinatorica 30.1 (2010): 83-104. Print.
  • Delhommé, Christian, Pouzet, Maurice, Sagi, Gabor and Sauer, Norbert. "Representation of ideals of relational structures". Discrete Mathematics 309.6 (2009): 1374-1384. Print.
  • Laflamme, Claude, Nguyen Van Thé, Lionel, Pouzet, Maurice and Sauer, Norbert. "Partitions and Indivisibility Properties of Countable Dimensional Vector Spaces". Jour. Comb. Theory, Series A 118.1 (2009): 67-77. Print.
  • Delhomme, Christian, Laflamme, Claude, Pouzet, Maurice and Sauer, Norbert. "Indivisible ultrametric spaces.". Topology Appl. 155.14 (2008): 1462–1478. Print.
  • Nguyen Van Thé, Lionel and Sauer, Norbert. "The Urysohn sphere is oscillation stable". GAFA (Geometric and Functional Analysis) (to appear), Print.
  • Nguyen Van Thé, Lionel and Sauer, Norbert. "Some weak indivisibility results in ultrahomogeneous metric spaces". submitted, (2008). Print.
  • Delhomme, Christian, Laflamme, Claude, Pouzet, Maurice and Sauer, Norbert. "Divisibility of countable metric spaces". European Journal of Combinatorics 28. (2007): 1746-1749. Print.
  • Sauer, Norbert. "Coloring subgraphs of the Rado graph". Combinatorica. An International Journal on Combinatorics and the Theory of Computing 26.2 (2006): 231-253. Print.
  • Sauer, Norbert. "Coloring subgraphs of the Rado graph". Combinatorica. An International Journal on Combinatorics and the Theory of Computing 26.2 (2006): 231-253. Print.
  • Sauer, Norbert. "Coloring subgraphs of the Rado graph". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 26.2 (2006). Print.
  • Sauer, Norbert, Sands, Bill, Duffus, Dwight and V. Rodl. "Chromatic numbers and homomorphisms of large girth hypergraphs". Algorithms and Combinatorics, Topics in Discrete Mathematics 26. (2006): 455-471. Print.
  • Pouzet, Maurice and Sauer, Norbert. "From well quasi-ordered sets to better quasi-ordered sets". The Electronic Journal of Combinatorics 13.1-3 (2006): 27. Print.
  • Sauer, Norbert and El-Zahar. "Indivisible homogeneous directed graphs and a game for vertex partitions". Discrete Math. 291.1-3 (2005): 99-113. Print.
  • Sauer, Norbert and M. El-Zahar. "Indivisible homogeneous directed graphs and a game for vertex partitions". Discrete Math. 291.1-3 (2005): 99-113. Print.
  • Duffus, Dwight and Sauer, Norbert. "Chromatic numbers and products". Discrete Math. 300.1-3 (2005): 91-99. Print.
  • Laflamme, Claude and Sauer, Norbert. "Canonical partitions of universal structures". Combinatorica. An International Journal on Combinatorics and the Theory of Computing 26.2 (2004): 183-205. Print.
  • Sauer, Norbert. "Canonical vertex partitions". Combinatorics, Probability and Computing 12.5-6 (2003): 671-704. Print.
  • Sauer, Norbert. "A {R}amsey theorem for countable homogeneous directed graphs". Discrete Math. 253.1-3 (2002): 45-61. Print.
  • Laviolette, Fran, Sauer, Norbert and Woodrow, Robert. "On cop-win graphs". Discrete Math. 258.1-3 (2002): 27-41. Print.
  • Delhomm{\'e}, Christian and Sauer, Norbert. "Homomorphisms of products of graphs into graphs without four cycles". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 22.1 (2002): 35-46. Print.
  • Kuich, Werner, Sauer, Norbert and Urbanek, Friedrich. "Heyting algebras and formal languages". J.UCS. The Journal of Universal Computer Science 8.7 (2002): 722-736 (electronic). Print.
  • Sauer, Norbert. "Hedetniemi's Conjecture-a survey". Discrete Math. 229.1-3 (2001): 261-292. Print.
  • Sauer, Norbert. "Hedetniemi's conjecture-a survey". Discrete Math. 229.1-3 (2001): 261-292. Print.
  • Sauer, Norbert. "Another look at the {E}rd{\H o}s-{H}ajnal-{P}\'osa results on partitioning edges and the {R}ado graph". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 21.2 (2001): 293-308. Print.
  • Kuich, Werner and Sauer, Norbert. "Atoms and partial orders of infinite languages". Theoretical Informatics and Applications. Informatique Th\'eorique et Applications 35.4 (2001): 389-401. Print.
  • Delhomm{\'e}, Christian, Pouzet, Maurice and Sauer, Norbert. "Jump-number of means on graphs". European Journal of Combinatorics 21.6 (2000): 767-775. Print.
  • Sauer, Norbert. "Edge partitions of the countable triangle free homogeneous graph". Discrete Math. 185.1-3 (1998): 137-181. Print.
  • Sauer, Norbert, Woodrow, Robert and R{\"o}dl, Vojtech. "Chromatic {R}amsey theory". European Journal of Combinatorics 18.1 (1997): 93-102. Print.
  • Duffus, Dwight and Sauer, Norbert. "Lattices arising in categorial investigations of {H}edetniemi's conjecture". Discrete Math. 152.1-3 (1996): 125-139. Print.
  • Pouzet, Maurice and Sauer, Norbert. "Edge partitions of the {R}ado graph". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 16.4 (1996): 505-520. Print.
  • Sauer, Norbert and {\v{S}}ir{\'a}{\v{n}}, Jozef. "The chromatic number of the union of two forests". Ars Combinatoria 42. (1996): 161-174. Print.
  • Wang, Hong and Sauer, Norbert. "Packing of three copies of a graph". Journal of Graph Theory 21.1 (1996): 71-80. Print.
  • Sauer, Norbert. "On the {R}amsey property of families of graphs". Transactions of the American Mathematical Society 347.3 (1995): 785-833. Print.
  • R{\"o}dl, V., Sauer, Norbert and Zhu, X.. "Ramsey families which exclude a graph". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 15.4 (1995): 589-596. Print.
  • El-Zahar, M. and Sauer, Norbert. "On the divisibility of homogeneous hypergraphs". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 14.2 (1994): 159-165. Print.
  • P{\"o}schel, R., Sapir, M. V., Sauer, Norbert, Stone, Mike and Volkov, M. V.. "Identities in full transformation semigroups". Algebra Universalis 31.4 (1994): 580-588. Print.
  • Droste, Manfred, Giraudet, Mich, Macpherson, Dugald and Sauer, Norbert. "Set-homogeneous graphs". Journal of Combinatorial Theory. Series B 62.1 (1994): 63-95. Print.
  • Wang, Hong and Sauer, Norbert. "Packing three copies of a tree into a complete graph". European Journal of Combinatorics 14.2 (1993): 137-142. Print.
  • Hajnal, A. and Sauer, Norbert. "Cut-sets in infinite graphs and partial orders". Discrete Math. 117.1-3 (1993): 113-125. Print.
  • Boroczky, K., Sauer, Norbert and Zhu, X.. "Inexhaustible homogeneous structures". Discrete Math. 115.1-3 (1993): 57-63. Print.
  • El-Zahar, M. and Sauer, Norbert. "On the divisibility of homogeneous directed graphs". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 45.2 (1993): 284-294. Print.
  • Kaiser, H. K. and Sauer, Norbert. "On order polynomially complete lattices". Algebra Universalis 30.2 (1993): 171-176. Print.
  • Gunderson, David, R{\"o}dl, Vojt and Sauer, Norbert. "Finite induced graph {R}amsey theory: on partitions of subgraphs". Journal of Combinatorial Theory. Series B 59.2 (1993): 199-209. Print.
  • Duffus, Dwight, R{\"o}dl, V., Sauer, Norbert and Woodrow, Robert. "Coloring ordered sets to avoid monochromatic maximal chains". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 44.1 (1992): 91-103. Print.
  • R{\"o}dl, V. and Sauer, Norbert. "The {R}amsey property for families of graphs which exclude a given graph". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 44.5 (1992): 1050-1060. Print.
  • Hor{\'a}k, Peter and Sauer, Norbert. "Covering complete graphs by cliques". Ars Combinatoria 33. (1992): 279-288. Print.
  • Sauer, Norbert and Zhu, X.. "An approach to {H}edetniemi's conjecture". Journal of Graph Theory 16.5 (1992): 423-436. Print.
  • Sauer, Norbert and Zhu, Xu. "Multiplicative posets". Order 8.4 (1991/92): 349-358. Print.
  • Pach, J. and Sauer, Norbert. "On the average volume of subsets in {E}uclidean {$d$}-space". European Journal of Combinatorics 12.5 (1991): 417-421. Print.
  • El-Zahar, M. and Sauer, Norbert. "Ramsey-type properties of relational structures". Discrete Math. 94.1 (1991): 1-10. Print.
  • Duffus, Dwight, Sands, Bill, Sauer, Norbert and Woodrow, Robert. "Two-colouring all two-element maximal antichains". Journal of Combinatorial Theory. Series A 57.1 (1991): 109-116. Print.
  • Sauer, Norbert and Stone, Mike. "Composing functions to reduce image size". Ars Combinatoria 31. (1991): 171-176. Print.
  • Sauer, Norbert and Stone, Mike. "Endomorphism monoids of algebras whose subalgebra lattices are chains". Algebra Universalis 28.2 (1991): 214-229. Print.
  • Sauer, Norbert and Stone, Mike. "On a problem of {B}. {J}\'onsson concerning subalgebras and endomorphisms". Algebra Universalis 27.3 (1990): 385-386. Print.
  • Gunderson, David, R{\"o}dl, Vojt and Sauer, Norbert. "Some results in finite graph {R}amsey theory". Congressus Numerantium. A Conference Journal on Numerical Themes 79. (1990): 232-243. Print.
  • Sauer, Norbert and Stone, Mike. "Foliations and applications to structure problems". Acta Mathematica Hungarica 53.1-2 (1989): 43-54. Print.
  • Sauer, Norbert and Stone, Mike. "Preemptive scheduling of interval orders is polynomial". Order 5.4 (1989): 345-348. Print.
  • El-Zahar, M. and Sauer, Norbert. "The indivisibility of the homogeneous {$K\sb n$}-free graphs". Journal of Combinatorial Theory. Series B 47.2 (1989): 162-170. Print.
  • El-Zahar, M. and Sauer, Norbert. "Asymptotic enumeration of two-dimensional posets". Order 5.3 (1988): 239-244. Print.
  • Duffus, Dwight and Sauer, Norbert. "Fixed points of products and the strong fixed point property". Order 4.3 (1987): 221-231. Print.
  • Sauer, Norbert and Stone, Mike. "Rational preemptive scheduling". Order 4.2 (1987): 195-206. Print.
  • Bialostocki, A. and Sauer, Norbert. "On {R}amsey-{T}ur\'an type problems in tournaments". Discrete Math. 59.3 (1986): 221-228. Print.
  • Hajnal, A. and Sauer, Norbert. "Complete subgraphs of infinite multipartite graphs and antichains in partially ordered sets". Discrete Math. 59.1-2 (1986): 61-67. Print.
  • El-Zahar, M. and Sauer, Norbert. "The chromatic number of the product of two {$4$}-chromatic graphs is {$4$}". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 5.2 (1985): 121-126. Print.
  • El-Zahar, Mohamed and Sauer, Norbert. "The length, the width and the cutset-number of finite ordered sets". Order 2.3 (1985): 243-248. Print.
  • Sauer, Norbert and Woodrow, Robert. "Finite cutsets and finite antichains". Order 1.1 (1984): 35-46. Print.
  • Sands, Bill, Sauer, Norbert and Woodrow, Robert. "On monochromatic paths in edge-coloured digraphs". Journal of Combinatorial Theory. Series B 33.3 (1982): 271-275. Print.
  • Milner, E. C. and Sauer, Norbert. "Remarks on the cofinality of a partially ordered set, and a generalization of {K}\"onig's lemma". Discrete Math. 35. (1981): 165-171. Print.
  • Milner, E. C. and Sauer, Norbert. "On chains and antichains in well-founded partially ordered sets". Journal of the London Mathematical Society. Second Series 24.1 (1981): 15-33. Print.
  • Birkenhead, R., Sauer, Norbert and Stone, Mike. "The algebraic representation of semigroups and lattices;\ representing lattice extensions". Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 43.3-4 (1981): 255-261. Print.
  • Sauer, Norbert and Stone, Mike. "The algebraic representation of semigroups and lattices;\ representing subsemigroups". Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 42.3-4 (1980): 313-323. Print.
  • Sauer, Norbert and Spencer, Joel. "Edge disjoint placement of graphs". Journal of Combinatorial Theory. Series B 25.3 (1978): 295-302. Print.
  • T{\'o}th, L. and Sauer, Norbert. "Thinnest packing of cubes with a given number of neighbours". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 20.4 (1977): 501-507. Print.
  • Sauer, Norbert and Stone, Mike. "Endomorphism and subalgebra structure; a concrete characterization". Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum 39.3-4 (1977): 397-402. Print.
  • Sauer, Norbert and Stone, Mike. "The algebraic closure of a function". Algebra Universalis 7.3 (1977): 295-306. Print.
  • Sauer, Norbert and Stone, Mike. "The algebraic closure of a semigroup of functions". Algebra Universalis 7.2 (1977): 219-233. Print.
  • Bollob{\'a}s, B and Sauer, Norbert. "Uniquely colourable graphs with large girth". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 28.6 (1976): 1340-1344. Print.
  • Erd{\H{o}}s, Paul, Sauer, Norbert, Schaer, Jonathan and Spencer, Joel. "Factorizing the complete graph into factors with large star number". J. Combinatorial Theory Ser. B 18. (1975): 180-183. Print.
  • Sauer, Norbert and Schaer, Jonathan. "On the factorization of the complete graph". J. Combinatorial Theory Ser. B 14. (1973): 1-6. Print.
  • Sauer, Norbert. "On the density of families of sets". J. Combinatorial Theory Ser. A 13. (1972): 145-147. Print.
  • Abbott, H. L., Hanson, D. and Sauer, Norbert. "Intersection theorems for systems of sets". J. Combinatorial Theory Ser. A 12. (1972): 381-389. Print.
  • Sauer, Norbert. "On the maximal number of edges in graphs with a given number of edge-disjoint triangles". Journal of the London Mathematical Society. Second Series 4. (1971): 153-156. Print.
  • Sauer, Norbert. "A generalization of a theorem of {T}ur\'an". J. Combinatorial Theory Ser. B 10. (1971): 109-112. Print.
  • Sauer, Norbert. "On the factorisation of the complete graph into factors of diameter {$2$}". J. Combinatorial Theory 9. (1970): 423-426. Print.
  • Sauer, Norbert. "On the existence of regular {$n$}-graphs with given girth". J. Combinatorial Theory 9. (1970): 144-147. Print.
  • Milner, E. C. and Sauer, Norbert. "Generalizations of a lemma of {F}olkman". Ann. New York Acad. Sci. 175. (1970): 295-307. Print.
  • Sauer, Norbert and Sch{\"o}nheim, J.. "Maximal subsets of a given set having no triple in common with a {S}teiner triple system on the set". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 12. (1969): 777-778. Print.
  • Sauer, Norbert. "Extremal point and edge sets in {$n$}-graphs". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 21. (1969): 1069-1075. Print.
  • Sauer, Norbert. "Extremaleigenschaften regul\"arer {G}raphen gegebener {T}aillenweite. {I}, {II}". \"Osterreich. Akad. Wiss. Math.-Natur. Kl. S.-B. II 176 (1967), 9-25; ibid. 176. (1967): 27-43. Print.

Preprint

  • Nguyen Van Thé, Lionel and Sauer, Norbert. "The Urysohn sphere is oscillation stable". , (2007). Print.