完全二部图的k-着色的重构

Pub Date : 2016-09-23 DOI:10.5666/KMJ.2016.56.3.647

Marcel Celaya, Kelly Choo, G. MacGillivray, K. Seyffarth

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引用次数: 10

摘要

设H为图，k≥χ(H)为整数。我们说H有k个着色的循环Gray编码，当且仅当有可能列出它的所有k个着色，使得连续着色，包括最后一个和第一个，在H的所有顶点上一致，除了一个。H的Gray码数是最小的整数k0(H)，使得H对所有k≥k0(H)都有其k色的循环Gray码。对于完全二部图，我们证明了当'和r都是奇数时k0(K '，r) = 3，否则k0(K '，r) = 4。

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Reconfiguring k-colourings of Complete Bipartite Graphs

Let H be a graph, and k ≥ χ(H) an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer k0(H) such that H has a cyclic Gray code of its k-colourings for all k ≥ k0(H). For complete bipartite graphs, we prove that k0(K`,r) = 3 when both ` and r are odd, and k0(K`,r) = 4 otherwise.

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