Minimum bull-saturated graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-07-14 DOI:10.1016/j.disc.2025.114674

Xinying Hua, Yuejian Peng

引用次数: 0

Abstract

For a given graph family

F

, a graph G is said to be

F

-saturated if G contains no member of

F

as a subgraph but the addition of any edge to G produces a member of

F

. If

F = {F}

, then G is said to be an F-saturated graph. The saturation number of F, denoted by

sat (n, F)

, is the minimum number of edges in an F-saturated graph with n vertices. A bull is the graph obtained by attaching two leaves to two vertices of a triangle. In this paper, we determine the saturation number of a bull and characterize corresponding minimum bull-saturated graphs.

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最小牛饱和图

对于给定的图族F，如果图G的子图中不包含F的元素，而G的任何边的加法产生F的一个元素，则称图G为F饱和图。如果F={F}，则称G为F饱和图。F的饱和数，用sat（n，F）表示，是具有n个顶点的F饱和图的最小边数。牛是通过将两个叶子连接到三角形的两个顶点而得到的图。本文确定了牛的饱和数，并刻画了相应的最小牛饱和图。

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.