A graph G = (V, E) with vertex set V and edge set E is called (a,b)-choosable (a ≥ 2b) if for any collection {L(υ)|υ ϵ V} of sets L(υ) of cardinality a ...
A graph G is (2m, m)-choosable if and only if its core is (am, m)-choosable. Trivially, the single vertex K1 is (2m,m)-choosable. Thus, we only need to consider.
Every 2-choosable graph is (2m, m)-choosable · Contents. Journal of Graph Theory. Volume 22, Issue 3 · PREVIOUS ARTICLE. The crossing number of C5 ×Cn. Previous ...
Every 2-choosable graph is (2 m, m )-choosable · Z. Tuza, M. Voigt · Published 1 July 1996 · Mathematics · Journal of Graph Theory.
Apr 27, 2014 · Confirming a special case of a conjecture of Erdős--Rubin--Taylor, Tuza and Voigt proved that 2-choosable graphs are (2m,m)-choosable for any ...
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Voigt, Every 2-choosable graph is (2m, m)-choosable, J. Graph The- ory, to appear. [9] V. G. Vizing, Coloring the vertices of a graph in prescribed colors (in ...
Here are some examples . Here is a proof that 02,2,2m is 2-choosable, for m 1 . Le t the assigned 2-sets be named as in the picture . Al and A2m+1 .
Apr 9, 2019 · Thus, for every bipartite graph G, there exists an m such that G is (2m, m)-choosable. It is easy to construct examples showing that m must ...
Recently, we proved this conjecture in the particular case a = 2 and b = 1, i.e., that every 2-choosable graph is (2m; m)-choosable for all m > 1 (see [17]).
Due to theorem 1.15, we need to prove that for every m ≥ 1, Θ2,2,2m is (4 : 2)-choosable. Suppose that m is odd and that m ≥ 3. Assume that Θ2,2,m−1 has vertex ...