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

Tara Abrishami; Eli Berger; Maria Chudnovsky; Shira Zerbib

doi:10.1016/j.ejc.2024.104035

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

Tara Abrishami, Eli Berger, Maria Chudnovsky, Shira Zerbib

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	104035
Journal	European Journal of Combinatorics
Volume	122
DOIs	https://doi.org/10.1016/j.ejc.2024.104035
State	Published - Dec 2024

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© 2024 Elsevier Ltd

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2024.104035

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title = "Graphs with no even holes and no sector wheels are the union of two chordal graphs",

abstract = "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.",

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AU - Abrishami, Tara

AU - Berger, Eli

AU - Chudnovsky, Maria

AU - Zerbib, Shira

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Y1 - 2024/12

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AB - 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.

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VL - 122

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

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

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