Cyclic base ordering of certain degenerate graphs

IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Xiaofeng Gu , Jessica Li , Eric H. Yang , William Y. Zhang
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引用次数: 0

Abstract

Let G be a connected graph. A cyclic base ordering of G is a cyclic ordering of elements in E(G) such that every cyclically consecutive |V(G)|1 edges form a spanning tree of G. The density of G is defined to be d(G)=|E(G)|/(|V(G)|1); and G is uniformly dense if d(H)d(G) for every connected subgraph H of G. It was conjectured by Kajitani, Ueno and Miyano that G has a cyclic base ordering if and only if G is uniformly dense. We show that the conjecture holds for maximal 2-degenerate graphs and graphs with uniform ear decompositions. As applications, book graphs, broken fan and broken wheel graphs have cyclic base ordering. We also study cyclic base ordering of double wheel graphs and the square of cycles.
某些退化图的环基排序
设 G 是一个连通图。G 的循环基序是 E(G) 中元素的循环排序,使得每个循环连续的 |V(G)|-1 边构成 G 的生成树。G 的密度定义为 d(G)=|E(G)|/(|V(G)|-1);如果对于 G 的每个连通子图 H,d(H)≤d(G),则 G 是均匀致密的。我们证明了这一猜想在最大 2-degenerate 图和具有均匀耳分解的图中成立。作为应用,书图、破扇图和破轮图都具有循环基序。我们还研究了双轮图的循环基序和循环平方。
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来源期刊
Discrete Applied Mathematics
Discrete Applied Mathematics 数学-应用数学
CiteScore
2.30
自引率
9.10%
发文量
422
审稿时长
4.5 months
期刊介绍: The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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