| Issue |
RAIRO-Oper. Res.
Volume 58, Number 6, November-December 2024
|
|
|---|---|---|
| Page(s) | 5369 - 5380 | |
| DOI | https://doi.org/10.1051/ro/2024064 | |
| Published online | 06 December 2024 | |
Integer k-matching preclusion of graphs
School of Mathematical Sciences, South China Normal University, Guangdong 510631, P.R. China
* Corresponding author: liuyan@scnu.edu.cn
Received:
20
July
2023
Accepted:
6
March
2024
As a generalization of matching preclusion number of a graph, we provide the (strong) integer k-matching preclusion number, abbreviated as MPk number (SMPk number), which is the minimum number of edges (vertices and edges) whose deletion results in a graph that has neither perfect integer k-matching nor almost perfect integer k-matching. In this paper, we obtain a necessary condition of graphs with an almost-perfect integer k-matching and a relational expression between the matching number and the integer k-matching number of bipartite graphs. And then the MPk number and the SMPk number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively.
Mathematics Subject Classification: 05C70 / 05C72 / 05C99
Key words: Integer k-matching / integer k-matching preclusion number / arrangement graphs
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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