TY - JOUR
T1 - Graphs with no even holes and no sector wheels are the union of two chordal graphs
AU - Abrishami, Tara
AU - Berger, Eli
AU - Chudnovsky, Maria
AU - Zerbib, Shira
N1 - Publisher Copyright:
© 2024 Elsevier Ltd
PY - 2024/12
Y1 - 2024/12
N2 - 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.
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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U2 - 10.1016/j.ejc.2024.104035
DO - 10.1016/j.ejc.2024.104035
M3 - Article
AN - SCOPUS:85199530367
SN - 0195-6698
VL - 122
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 104035
ER -