Disconnected forbidden pairs force supereulerian graphs to be hamiltonian

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-31 DOI:10.1016/j.disc.2024.114301

Qiang Wang , Liming Xiong

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引用次数: 0

Abstract

A graph is said to be supereulerian if it has a spanning eulerian subgraph, i.e., a spanning connected even subgraph. A graph is called hamiltonian if it contains a spanning cycle. A graph is said to be

{R, S}

-free if it does not contain R or S as an induced subgraph. Yang et al. characterized all pairs of connected graphs

R, S

such that every supereulerian

{R, S}

-free graph is hamiltonian. In this paper, we consider disconnected forbidden graph

R, S

. We characterize all pairs of disconnected graphs

R, S

such that every supereulerian

{R, S}

-free graph of sufficiently large order is hamiltonian. Applying this result, we also characterize all forbidden pairs for the existence of a Hamiltonian cycle in 2-edge connected graphs.

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断开的禁止对迫使超立体图成为哈密顿图

如果一个图有一个跨越的优勒子图，即一个跨越的连通偶数子图，则称该图为超优勒图。如果一个图包含一个跨循环，则称为哈密顿图。如果一个图不包含 R 或 S 作为诱导子图，则称其为无{R,S}图。Yang等人描述了所有连通图R,S的特征，即每个无超循环{R,S}图都是哈密顿图。在本文中，我们考虑断开的禁止图 R,S。我们描述了所有成对的断开图 R,S 的特征，即每个阶数足够大的无超线性 {R,S} 图都是哈密顿图。应用这一结果，我们还描述了在 2 边相连图中存在哈密顿循环的所有禁止图对。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.