Detecting K_2,3 as an induced minor
arxiv(2024)
摘要
We consider a natural generalization of chordal graphs, in which every
minimal separator induces a subgraph with independence number at most 2. Such
graphs can be equivalently defined as graphs that do not contain the complete
bipartite graph K_2,3 as an induced minor, that is, graphs from which
K_2,3 cannot be obtained by a sequence of edge contractions and vertex
deletions.
We develop a polynomial-time algorithm for recognizing these graphs. Our
algorithm relies on a characterization of K_2,3-induced minor-free graphs
in terms of excluding particular induced subgraphs, called Truemper
configurations.
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