Graphs with no even holes and no sector wheels are the union of two chordal graphs

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2024
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  • Sivaraman (2020) conjectured that if G is a graph with no induced even cycle then there exist sets X1,X2⊆V(G) satisfying V(G)=X1∪X2 such that the induced graphs G[X1] and G[X2] are both chordal. We prove this conjecture in the special case where G contains no sector wheel, namely, a pair (H,w) where H is an induced cycle of G and w is a vertex in V(G)∖V(H) such that N(w)∩H is either V(H) or a path with at least three vertices. © 2024 Elsevier Ltd
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  • info:eu-repo/semantics/closedAccess
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oai:www.edit.fis.uni-hamburg.de:publications/6ee67d1b-f9e1-44a2-8759-360c6c48c241