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- W2132677029 abstract "A Kl-expansion consists of l vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion odd if its vertices can be two-coloured so that the edges of the trees are bichromatic but the edges between trees are monochromatic. We show that, for every l, if a graph contains no odd Kl-expansion then its chromatic number is O(llogl). In doing so, we obtain a characterization of graphs which contain no odd Kl-expansion which is of independent interest. We also prove that given a graph and a subset S of its vertex set, either there are k vertex-disjoint odd paths with endpoints in S, or there is a set X of at most 2k−2 vertices such that every odd path with both ends in S contains a vertex in X. Finally, we discuss the algorithmic implications of these results." @default.
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- W2132677029 date "2009-01-01" @default.
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- W2132677029 title "On the odd-minor variant of Hadwiger's conjecture" @default.
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- W2132677029 doi "https://doi.org/10.1016/j.jctb.2008.03.006" @default.
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