论文信息 - Coloring digraphs by iterated antichains

Coloring digraphs by iterated antichains

We show that the minimum chromatic number of a product of two n-chromatic graphs is either bounded by 9, or tends to infinity. The result is obtained by the study of coloring iterated adjoints of a digraph by iterated antichains of a poset.

Svatopluk Poljak

[1] Daniel Turzík. A note on chromatic number of direct product of graphs , 1983 .

[2] R. P. Dilworth. Some Combinatorial Problems on Partially Ordered Sets , 1990 .

[3] Pavol Hell,et al. On multiplicative graphs and the product conjecture , 1988, Comb..

[4] Roger C. Entringer,et al. Arc Colorings of Digraphs , 1972 .

[5] Dwight Duffus,et al. On the chromatic number of the product of graphs , 1985, J. Graph Theory.

[6] S. Hedetniemi. Homomorphisms of graphs and automata , 1967 .

[7] Norbert Sauer,et al. The chromatic number of the product of two 4-chromatic graphs is 4 , 1985, Comb..

[8] Svatopluk Poljak,et al. On the arc-chromatic number of a digraph , 1981, J. Comb. Theory, Ser. B.