Chromatic Numbers of Products of Tournaments: FractionalAspects of Hedetniemi's Conjecture
نویسنده
چکیده
The chromatic number of the categorical product of two n-tournaments can be strictly smaller than n. We show that min{χ(S × T ) : S and T are n-tournaments} is asymptotically equal to λn, where 12 ≤ λ ≤ 2 3 .
منابع مشابه
[gtn Liv:6] Hedetniemi’s Conjecture, 40 Years Later
Hedetniemi’s conjecture states that the chromatic number of a categorical product of graphs is equal to the minimum of the chromatic numbers of the factors. We survey the many partial results surrounding this conjecture, to review the evidence and the counter evidence.
متن کاملHedetniemi’s conjecture and fiber products of graphs
We prove that for n ≥ 4, a fiber product of n-chromatic graphs over n-colourings can have chromatic number strictly less than n. This refutes a conjecture of Y. Carbonneaux, S. Gravier, A. Khelladi, A. Semri, Coloring fiber product of graphs. AKCE Int. J. Graphs Comb. 3 (2006), 59–64.
متن کاملA Survey on Hedetniemi’s Conjecture
More than 30 years ago, Hedetniemi made a conjecture which says that the categorical product of two n-chromatic graphs is still n-chromatic. The conjecture is still open, despite many different approaches from different point of views. This article surveys methods and partial results; and discuss problems related to or motivated by this conjecture.
متن کاملInterlacing adjoints on directed graphs
For an integer k ≥ 1, the k-th interlacing adjoint of a digraph G is the digraph ιk(G) with vertex-set V (G) k , and arcs ((u1, . . . , uk), (v1, . . . , vk)) such that (ui, vi) ∈ A(G) for i = 1, . . . , k and (vi, ui+1) ∈ A(G) for i = 1, . . . , k − 1. For every k we derive upper and lower bounds for the chromatic number of ιk(G) in terms of that of G. In particular, we find tight bounds on th...
متن کاملHedetniemi’s Conjecture Via Alternating Chromatic Number
In an earlier paper, the present authors (2013) [1] introduced the alternating chromatic number for hypergraphs and used Tucker’s Lemma, an equivalent combinatorial version of the Borsuk-Ulam Theorem, to show that the alternating chromatic number is a lower bound for the chromatic number. In this paper, we determine the chromatic number of some families of graphs by specifying their alternating...
متن کامل