Critical Vertices and Edges in $H$-free Graphs
نویسندگان
چکیده
A vertex or edge in a graph is critical if its deletion reduces the chromatic number of the graph by 1. We consider the problems of deciding whether a graph has a critical vertex or edge, respectively. We give a complexity dichotomy for both problems restricted to H-free graphs, that is, graphs with no induced subgraph isomorphic to H. Moreover, we show that an edge is critical if and only if its contraction reduces the chromatic number by 1. Hence, we also obtain a complexity dichotomy for the problem of deciding if a graph has an edge whose contraction reduces the chromatic number by 1.
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عنوان ژورنال:
- CoRR
دوره abs/1706.09043 شماره
صفحات -
تاریخ انتشار 2017