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- W4300106401 abstract "Let $G$ be a simple graph with vertex set $V(G)$. A set $Ssubseteq V(G)$ is independent if no two vertices from $S$ are adjacent. For $Xsubseteq V(G)$, the difference of $X$ is $d(X) = |X|-|N(X)|$ and an independent set $A$ is critical if $d(A) = max {d(X): Xsubseteq V(G) text{ is an independent set}}$ (possibly $A=emptyset$). Let $text{nucleus}(G)$ and $text{diadem}(G)$ be the intersection and union, respectively, of all maximum size critical independent sets in $G$. In this paper, we will give two new characterizations of K{o}nig-Egerv'{a}ry graphs involving $text{nucleus}(G)$ and $text{diadem}(G)$. We also prove a related lower bound for the independence number of a graph. This work answers several conjectures posed by Jarden, Levit, and Mandrescu." @default.
- W4300106401 created "2022-10-03" @default.
- W4300106401 creator A5000099737 @default.
- W4300106401 date "2015-09-16" @default.
- W4300106401 modified "2023-09-28" @default.
- W4300106401 title "On some conjectures concerning critical independent sets of a graph" @default.
- W4300106401 doi "https://doi.org/10.48550/arxiv.1509.05057" @default.
- W4300106401 hasPublicationYear "2015" @default.
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