Lattices arising in categorial investigations of Hedetniemi's conjecture

Discrete Mathematics

Volumn 152, Issue 1-3, 1996, Pages 125-139

  Duffus, Dwight ^a   Sauer, Norbert ^b  

^a EMORY UNIVERSITY   (United States)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Hedetniemi conjecture; Multiplicative structures in categories; Product

Indexed keywords

EID: 0000257011     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0012-365X(94)00298-W     Document Type: Article

References (21)

1. G. Birkhoff, Extended arithmetic, Duke Math. J. 3 (1937) 311-316.
2. G. Birkhoff, Generalized arithmetic, Duke Math. J. 9 (1942) 283-302.
3. D. Duffus, B. Sands and R. Woodrow, On the chromatic number of the product of graphs. J. Graph Theory 9 (1985) 487-495.
4. M.H. El-Zahar and N.W. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4, Combinatorica 5 (1985) 121-126.
5. G. Grätzer, Lattice Theory (W.H. Freeman and Company, San Francisco, 1971).
6. R. Haggkvist, P. Hell, D.J. Miller and V.N. Lara, On multiplicative graphs and the product conjecture, Combinatrica 8 (1988) 63-74.
7. 1-chromatic graphs can be countable, Combinatorica 5 (1985) 137-140.
8. S. Hedetniemi, Homomorphisms of graphs and automata, Univ. of Michigan Technical Report 03105-44-T, 1966.
9. P. Hell, H. Zhou and X. Zhu, Homomorphisms to Oriented Cycles, Combinatorica, to appear.
10. N.W.H. Herrlich and E. Strecker, Category Theory (Allyn and Bacon, Newton, MA, 1973).
11. L. Lovasz, Operations with structures, Acta. Math. Acad. Sci. Hung. (1967) 321-328.
12. D.J. Miller, The categorical product of graphs, Can. J. Math. 20 (1968) 1511-1521.
13. R. Paré, Co-limits in topoi, Bull. Am. Math. Soc. 80 (1974) 556-561.
14. S. Poljak and V. Rödl, On the arc-chromatic number of a digraph. JCT B 31 (1981) 190-198.
15. S. Poljak, Coloring digraphs by iterated antichains. Comment. Math. Univ. Carolinae 32 (1991) 209-212.
16. H. Rasiowa and R. Sikorski, The Mathemaatics of Metamathematics (Polish Scientific Publishers, 1963).
17. H. Rasiowa, An Algebraic Approach to Non-Classical Logics (North-Holland, Amsterdam, 1974).
18. G. Sabidussi, Graph multiplication, Math. Z. 72 (1960) 446-457.
19. N.W. Sauer and X. Zhu, Multiplicative Posets, ORDER, to appear.
20. N.W. Sauer and X. Zhu, An approach to Hedetniemi's conjecture, J. Graph Theory, to appear.
21. E. Welzl, Color-families are dense, Theoret. Comput. Sci. 17 (1982) 29-41.