极小不可扩预着色与隐关系
Minimal non-extensible precolorings and implicit-relations
摘要：
在本文中，我研究了一个变种的一般顶点着色问题称为预着色。具体来说，我研究图预着色，通过发展新的理论，用于表征最小的不可扩展预着色。有趣的是，对于任意大色数的图，在不可扩展的预着色中，着色顶点的最小数目保持不变;只有两个顶点$u,v$就足够了。这里，这种$u,v$之间的关系被称为隐关系，区分两种情况：（i）隐边，其中$u,v$被预着色为相同的颜色;和（ii）隐恒等式，其中$u,v$被预着色为不同的。
英文摘要：
In this paper I study a variant of the general vertex coloring problem called precoloring. Specifically, I study graph precolorings, by developing new theory, for characterizing the minimal non-extensible precolorings. It is interesting per se that, for graphs of arbitrarily large chromatic number, the minimal number of colored vertices, in a non-extensible precoloring, remains constant; only two vertices $u,v$ suffice. Here, the relation between such $u,v$ is called an implicit-relation, distinguishing two cases: (i) implicit-edges where $u,v$ are precolored with the same color and (ii) implicit-identities where $u,v$ are precolored distinct.
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