منابع مشابه
A Fractional Analogue of Brooks' Theorem
Let ∆(G) be the maximum degree of a graph G. Brooks’ theorem states that the only connected graphs with chromatic number χ(G) = ∆(G) + 1 are complete graphs and odd cycles. We prove a fractional analogue of Brooks’ theorem in this paper. Namely, we classify all connected graphs G such that the fractional chromatic number χf (G) is at least ∆(G). These graphs are complete graphs, odd cycles, C 2...
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Let m(n) be the maximum integer such that every partially ordered set P with n elements contains two disjoint subsets A and B, each with cardinality m(n), such that either every element of A is greater than every element of B or every element of A is incomparable with every element of B. We prove that m(n) = Θ( n logn). Moreover, for fixed ǫ ∈ (0, 1) and n sufficiently large, we construct a par...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2004.04.017