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arXiv · 1606.06370

Independence and matching numbers of some token graphs

Hernan de Alba·Walter Carballosa·Jesús Leaños·Luis Manuel Rivera
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Abstract

Let $G$ be a graph of order $n$ and let $k\in\{1,\ldots,n-1\}$. The $k$-token graph $F_k(G)$ of $G$, is the graph whose vertices are the $k$-subsets of $V(G)$, where two vertices are adjacent in $F_k(G)$ whenever their symmetric difference is an edge of $G$. We study the independence and matching numbers of $F_k(G)$. We present a tight lower bound for the matching number of $F_k(G)$ for the case in which $G$ has either a perfect matching or an almost perfect matching. Also, we estimate the independence number for bipartite $k$-token graphs, and determine the exact value for some graphs.

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Hernan de Alba, Walter Carballosa, Jesús Leaños, Luis Manuel Rivera. 2016-06-21. Independence and matching numbers of some token graphs. https://arxiv.org/abs/1606.06370

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