The sandwich problem for odd-hole-free and even-hole-free graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-01-08 DOI:10.1016/j.disc.2024.114383

Kathie Cameron , Aristotelis Chaniotis , Celina M.H. de Figueiredo , Sophie Spirkl

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引用次数: 0

Abstract

For a property

P

of graphs, the

P

-Sandwich-Problem, introduced by Golumbic and Shamir (1993), is the following: Given a pair of graphs

(G_{1}, G_{2})

on the same vertex set V, does there exist a graph G such that

V (G) = V

E (G_{1}) \subseteq E (G) \subseteq E (G_{2})

, and G satisfies

P

? A hole in a graph is an induced subgraph which is a cycle of length at least four. An odd (respectively even) hole is a hole of odd (respectively even) length. Given a class of graphs

C

and a graph G we say that G is

C

-free if it contains no induced subgraph isomorphic to a member of

C

. In this paper we prove that if

P

is the property of being odd-hole-free or the property of being even-hole-free, then the

P

-Sandwich-Problem is

NP

-complete.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.