Research:


I do research in graph theory, most specifically in graph homomorphisms, finite duality and Hedetniemi's conjecture.

Survey Papers:

C. Tardif,  Hedetniemi's conjecture, 40 years later (pdf 115KB), Graph Theory Notes of New York LIV, 46-57 (2008), New York Academy of Sciences. updates

G. Hahn, C. Tardif, Graph homomorphisms: structure and symmetry (pdf 502KB), Graph symmetry (Montreal, PQ, 1996), 107-166, NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences 497, Kluwer Academic Publishers, Dordrecht, 1997.

Preprints:

D. Rorabaugh, C. Tardif, D. Wehlau, I. Zaguia, Iterated arc graphs (arxiv), 2016, 7 pages MS.

J. Foniok, C. Tardif Hedetniemi's conjecture and adjoint functors in thin categories (arxiv), 2016, 17 pages MS.

G. Simons, C. Tardif, D. Wehlau, Topologically 4-chromatic graphs and signatures of odd cycles (arxiv), 2016, 15 pages MS.

C. Tardif, A single transferable reservation model for public transportation (pdf 170KB), preprint, 2014, 17 pages MS.

Research Papers:

P. L. Erdős, D. Pálvölgyi, C. Tardif, G. Tardos, Regular families of forests, antichains and duality pairs of relational structures, Combinatorica 37, (2017), 651-672.

D. Rorabaugh, C. Tardif, D.Wehlau, Logical compactness and constraint satisfaction problems, Logical Methods in Computer Science, Volume 13, Issue 1 (2017), 11 pp. (electronic).

G. Simons, C. Tardif, D. Wehlau, Generalised Mycielski graphs, signature systems, and bounds on chromatic numbers, Journal of Combinatorial Theory Series B 122 (2017), 776-793.

K. Jao, C. Tardif, D. West, X. Zhu, Circular chromatic Ramsey number Journal of Combinatorics, 8 (2017), 189-208.

L. Beaudou, R. Naserasr, C. Tardif, Homomorphisms of binary Cayley graphs, Discrete Mathematics 338 (2015), 2539-2544.

J. Bosica, C. Tardif, Fractional aspects of the Erdős-Faber-Lovász conjecture, Discussiones Mathematicae Graph Theory 35 (2015), 197-202.

J. Foniok, C. Tardif, Digraph functors which admit both left and right adjoints, Discrete Mathematics 338 (2015), 527-535.

T. Feder, P. Hell, B. Larose, M. Siggers, C. Tardif, Graphs admitting k-NU operations Part II: The Irreflexive Case, SIAM J. Discrete Math. 28 (2014) no. 2, 817-834.

T. Feder, P. Hell, B. Larose, C. Loten, M. Siggers, C. Tardif, Graphs admitting k-NU operations. Part I: The Reflexive Case, SIAM J. Discrete Math. 27 (2013), no. 4, 1940-1963.

P. L. Erdős, C. Tardif, G. Tardos, Caterpillar dualities and regular languages (pdf 256KB), SIAM J. Discrete Math. 27 (2013), 1287-1294.

P. L. Erdős, C. Tardif, G. Tardos, On infinite-finite duality pairs of directed graphs, Order 30(3) (2013), 807-819.

G. Simonyi, C. Tardif, A. Zsbán, Colourful theorems and topological lower bounds on chromatic numbers, Electronic Journal of Combinatorics 20(1) (2013), paper 10, 15 pages.

C. Tardif, I. Zaguia, Hedetniemi's conjecture and fiber products of graphs, AKCE Int. J. Graphs Comb. 9 (2012), 53-58.

N. Paul, C. Tardif, The chromatic Ramsey number of odd wheels, Journal of Graph Theory 69 (2012), 198-205.

J. Foniok, J. Nešetřil, C. Tardif, Interleaved adjoints on directed graphs European Journal of Combinatorics 32 (2011), 1018-1024.

C. Loten, C. Tardif, Near-unanimity polymorphisms on structures with finite duality (pdf 120KB), SIAM J. Discrete Math. 25 (2011), 490-496.

C. Tardif, Hedetniemi's conjecture and dense boolean lattices, Order 28 (2011), 181-191.

A. Bonato, G. Hahn, C. Tardif, Large classes of infinite k-cop-win graphs, Journal of Graph Theory 65 (2010), 334-342.

J. Foniok, J. Nešetřil, A. Pultr, and C. Tardif. Dualities and dual pairs in Heyting algebras, Order 27 (2010), 327-342.

G. Kun, C. Tardif, Homomorphisms of random paths, European Journal of Combinatorics 31 (2010), 688-693.

J. Nešetřil, C. Tardif, Path homomorphisms, graph colourings and boolean matrices, Journal of Graph Theory 63 (2010), 198-209.

J. Foniok, C. Tardif, Adjoint functors and tree duality, Discrete Mathematics & Theoretical Computer Science, Vol 11, No 2 (2009), 97-110.

Z. Che, K. L. Collins, C. Tardif, Odd-angulated graphs and cancelling factors in box products. Journal of Graph Theory 58  (2008), 221-238.

C. Loten, C. Tardif, Majority functions on structures with finite duality, European Journal of Combinatorics 29 (2008), 979-986.

J. Foniok, J. Nešetřil, C. Tardif, Generalised dualities and maximal finite antichains in the homomorphism order of relational structures, European Journal of Combinatorics 29 (2008), 881-899.

J. Nešetřil, C. Tardif, A dualistic approach to bounding the chromatic number of a graph. European Journal of Combinatorics 29 (2008), 254-260.

B. Larose, C. Loten, C. Tardif, A characterisation of first-order constraint satisfaction problems, Logical Methods in Computer Science 3 (2007), no. 4, 4:6, 22 pp. (electronic).

J. Nešetřil, A. Pultr, C. Tardif, Gaps and dualities in Heyting categories, Commentationes Mathematicae Universitatis Carolinae 48 (2007), 9-23.

J. Foniok, J. Nešetřil, C. Tardif, Generalised dualities and finite maximal antichains, Graph-theoretic concepts in computer science, 27-36, Lecture Notes in Computer Science, 4271, Springer, Berlin, 2006.

A. Bonato, C. Tardif, Mutually embeddable graphs and the tree alternative conjecture, Journal of Combinatorial Theory Series B 96 (2006), 874-880.

B. Larose, C. Loten, C. Tardif, A Characterisation of First-Order Constraint Satisfaction Problems. LICS 2006: 201-210.

C. Tardif, On the Algorithmic Aspects of Hedetniemi's Conjecture (pdf 74KB), in Topics in Discrete Mathematics (M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas, P. Valtr eds.), Algorithms and Combinatorics 26 (2006), 355-358.

R. Naserasr, C. Tardif, The chromatic covering number of a graph, Journal of Graph Theory 51 (2006), 199-204.

C.Tardif, D. Wehlau, Chromatic numbers of products of graphs: the directed and undirected versions of the Poljak-Rödl function, Journal of Graph Theory 51 (2006), 33-36.

J. Nešetřil, C.Tardif, Short answers to exponentially long questions: extremal aspects of homomorphism duality, SIAM Journal on Discrete Mathematics 19 (2005), 914-920.

C. Tardif, The fractional chromatic number of the categorical product of graphs, Combinatorica 25 (2005), 625-632.

C. Tardif, Multiplicative graphs and semi-lattice endomorphisms in the category of graphs, Journal of Combinatorial Theory Ser. B 95 (2005), 338-345.

L. Haddad, C. Tardif, A Clone-theoretic formulation of the Erdős-Faber-Lovász conjecture, Discussiones Mathematicae Graph Theory 24 (2004), 545-549.

A. Coté, V. Chouinard-Prévost, C. Tardif, Orientations and 3-colourings of graphs, Commentationes Mathematicae Universitatis Carolinae 45 (2004), 549-553.

B. Larose, C. Tardif, A discrete homotopy theory for reflexive structures, Advances in Mathematics 189 (2004), 268-300.

C. Tardif, Chromatic numbers of products of tournaments: Fractional aspects of Hedetniemi's conjecture (pdf 120 Kb), Graphs, morphisms and statistical physics, 171-175, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 63 (2004), American Mathematical Society, Providence, RI.

J. Nešetřil, C Tardif, On maximal finite antichains in the homomorphism order of directed graphs, Discussiones Mathematicae Graph Theory 23 (2003), 325-332.

A. Bonato, C. Tardif, Large families of mutually embeddable vertex-transitive graphs. J. Graph Theory 43 (2003), 99-106.

J. Nešetřil, C Tardif, Density via duality. Algorithms (Prague, 1999). Theoretical Computer Science 287 (2002), 585-591.

B. Larose, C. Tardif, Projectivity and independent sets in powers of graphs. Journal of Graph Theory 40 (2002), 162-171.

C. Tardif, X. Zhu, On Hedetniemi's conjecture and the colour template scheme, Discrete Mathematics 253 (2002), 77-85.

C. Tardif, X. Zhu, The level of nonmultiplicativity of graphs, Discrete Mathematics 244 (2002), 461-471.

B. Larose, C. Tardif, Strongly rigid graphs and projectivity, Multiple-Valued Logic 7 (2001), 339-361.

C. Tardif, Fractional chromatic numbers of cones over graphs, Journal of Graph Theory 38 (2001), 87-94.

C. Tardif, The chromatic number of the product of two graphs is at least half the minimum of the fractional chromatic numbers of the factors, Commentationes Mathematicae Universitatis Carolinae 42 (2001), 353-355.

B. Larose, C. Tardif, Hedetniemi's conjecture and the retracts of a product of graphs, Combinatorica 20 (2000), 531-544.

J. Nešetřil, C. Tardif, Duality theorems for finite structures (characterising gaps and good characterisations), Journal of Combininatorial Theory Series B 80 (2000), 80-97.

J. Nešetřil, C. Tardif, Density, Contemporary trends in discrete mathematics (Stirin Castle, 1997), 229-235, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 49, American Mathematical Society, Providence, RI, 1999.

C. Tardif, Fractional multiples of graphs and the density of vertex-transitive graphs, Journal of Algebraic Combinatorics 10 (1999), 61-68.

B. Larose, F. Laviolette, C. Tardif, On normal Cayley graphs and hom-idempotent graphs, European Journal of Combinatorics 19 (1998), 867-881.

C. Tardif, Homomorphismes du graphe de Petersen et inegalites combinatoires, Annales des Sciences Mathematiques du Quebec 22 (1998), 87-94.

C. Tardif, Graph products and the chromatic difference sequence of vertex-transitive graphs, Discrete Mathematics 185 (1998), 193-200.

C. Tardif, A fixed box theorem for the Cartesian product of graphs and metric spaces, Discrete Mathematics 171 (1997), 237-248.

C. Tardif, On compact median graphs, Journal of Graph Theory 23 (1996), 325-336.

C. Tardif, Prefibers and the Cartesian product of metric spaces, Discrete Mathematics 109 (1992), 283-288.

Articles éducatifs sur les systèmes électoraux:

C. Tardif, Mathematical aspects of electoral systems, Pi in the Sky 19 (2015), 12-18.

C. Tardif, Les systèmes électoraux : Le vote unique transférable (pdf 283KB), Envol 155 (2011), 19-23.

C. Tardif, Les systèmes électoraux : La représentation proportionnelle (pdf 646KB), Envol 153 (2010), 7-10.

C. Tardif, Les systèmes électoraux dans le monde et en classe (pdf 263KB), Envol 152 (2010), 43-47.


Students and Postdoctoral Fellows

Master's degree

Postdoctoral fellows