路径图的两个新表征

SIAM J. Discret. Math. Pub Date : 2022-08-01 DOI:10.48550/arXiv.2208.01001

N. Apollonio, Lorenzo Balzotti

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引用次数: 0

摘要

路径图是树中路径的交点图。本文从Monma和Wei [C.L.~Monma，~and~V.K.]对路径图的表征入手~Wei，树中路径的相交图，J. Combin。Ser的理论。B, 41:2(1986) 141—181]并将其简化为一些2-着色子问题，获得了直接导致多项式识别算法的第一个表征。然后，我们引入了图的附属图的集合，并给出了每个附属图中最小禁止2边彩色子图的列表。

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Two New Characterizations of Path Graphs

Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181] and we reduce it to some 2-colorings subproblems, obtaining the first characterization that directly leads to a polynomial recognition algorithm. Then we introduce the collection of the attachedness graphs of a graph and we exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the attachedness graph.

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SIAM J. Discret. Math.

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