On the length of L-Grundy sequences

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-08-01 DOI:10.1016/j.disopt.2022.100725

Rebekah Herrman , Stephen G.Z. Smith

引用次数: 2

Abstract

An L-sequence of a graph $G$ is a sequence of distinct vertices $S = (v_{1}, \dots, v_{k})$ such that $N [v_{i}] ∖ \cup_{j = 1}^{i - 1} N (v_{j}) \neq 0̸$ . The length of a longest L-sequence is called the L-Grundy domination number, denoted $γ_{g r}^{L} (G)$ . In this paper, we prove $γ_{g r}^{L} (G) \leq n (G) - δ (G) + 1$ , which was conjectured by Brešar, Gologranc, Henning, and Kos. We also prove some initial results about characteristics of $n$ -vertex graphs satisfying $γ_{g r}^{L} (G) = n$ .

查看原文本刊更多论文

关于L-Grundy序列的长度

图G的l序列是由不同顶点S=(v1，…，vk)组成的序列，使得N[vi]∈∪j=1i−1N(vj)≠0 ε。最长l序列的长度称为L-Grundy支配数，记为γgrL(G)。本文证明了Brešar、Gologranc、Henning和Kos猜想的γgrL(G)≤n(G)−δ(G)+1。我们还证明了n顶点图满足γgrL(G)=n的一些初步结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.