The saturation number of C6

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-03 DOI:10.1016/j.disc.2025.114504

Yongxin Lan , Yongtang Shi , Yiqiao Wang , Junxue Zhang

引用次数: 0

Abstract

A graph G is called

C_{k}

-saturated if G is

C_{k}

-free but

G + e

is not for any

e \in E (\overline{G})

. The saturation number of

C_{k}

, denoted

s a t (n, C_{k})

, is the minimum number of edges in a

C_{k}

-saturated graph on n vertices. Finding the exact values of

s a t (n, C_{k})

has been one of the most intriguing open problems in extremal graph theory. In this paper, we study the saturation number of

C_{6}

. We prove that

4 n / 3 - 2 \leq s a t (n, C_{6}) \leq (4 n + 1) / 3

for all

n \geq 9

, which significantly improves the existing lower and upper bounds for

s a t (n, C_{6})

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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.