The saturation number for unions of four cliques

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-10 DOI:10.1016/j.disc.2025.114532

Ruo-Xuan Li, Rong-Xia Hao, Zhen He, Wen-Han Zhu

引用次数: 0

Abstract

A graph G is H-saturated if G does not contain a copy of H, but the addition of any edge

e \in \overline{G}

would create a copy of H. The saturation number

s a t (n, H)

for a graph H is the minimal number of edges in any H-saturated graph of order n. The

s a t (n, K_{p_{1}} \cup K_{p_{2}} \cup K_{p_{3}})

with

p_{3} \geq p_{1} + p_{2}

was determined in [Discrete Math. 347 (2024) 113868]. In this paper,

s a t (n, K_{p_{1}} \cup K_{p_{2}} \cup K_{p_{3}} \cup K_{p_{4}})

with

p_{i + 1} - p_{i} \geq p_{1}

for

2 \leq i \leq 3

and

4 \leq p_{1} \leq p_{2}

is determined.

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四团联合的饱和数

图G是H饱和的，如果G不包含H的副本，但是任何边e∈G的加法都会产生H的副本。图H的饱和数sat（n，H）是任何n阶H饱和图中最小的边数。p3≥p1+p2的sat（n,Kp1∪Kp2∪Kp3）在[离散数学。347(2024)113868]中确定。本文求出了当2≤i≤3且4≤p1≤p2时，π +1−π≥p1的sat（n,Kp1∪Kp2∪Kp3∪Kp4）。

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.