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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.more » « lessFree, publicly-accessible full text available December 1, 2025
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Berger, Eli; Seymour, Paul (, Combinatorica)
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Berger, Eli; Choromanski, Krzysztof; Chudnovsky, Maria; Zerbib, Shira (, European Journal of Combinatorics)
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Berger, Eli; Seymour, Paul; Spirkl, Sophie (, Discrete Mathematics)null (Ed.)
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