Generalization of matching extensions in graphs (II)
| dc.creator | Jin, Zemin | |
| dc.creator | Yan, Huifang | |
| dc.creator | Yu, Qinglin | |
| dc.date | 2006-09-27 | |
| dc.date.accessioned | 2026-07-07T07:25:18Z | |
| dc.date.available | 2026-07-07T07:25:18Z | |
| dc.description | Proposed as a general framework, Liu and Yu(Discrete Math. 231 (2001) 311-320) introduced $(n,k,d)$-graphs to unify the concepts of deficiency of matchings, $n$-factor-criticality and $k$-extendability. Let $G$ be a graph and let $n,k$ and $d$ be non-negative integers such that $n+2k+d\leq |V(G)|-2$ and $|V(G)|-n-d$ is even. If when deleting any $n$ vertices from $G$, the remaining subgraph $H$ of $G$ contains a $k$-matching and each such $k$- matching can be extended to a defect-$d$ matching in $H$, then $G$ is called an $(n,k,d)$-graph. In \cite{Liu}, the recursive relations for distinct parameters $n, k$ and $d$ were presented and the impact of adding or deleting an edge also was discussed for the case $d = 0$. In this paper, we continue the study begun in \cite{Liu} and obtain new recursive results for $(n,k,d)$-graphs in the general case $d \geq0$. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609756 | |
| dc.identifier | http://arxiv.org/abs/math/0609756 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116672 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C70 | |
| dc.title | Generalization of matching extensions in graphs (II) | |
| dc.type | text |