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- W4375870085 abstract "For a graph $G$ with the vertex set $V(G)$ and the edge set $E(G)$ and a star subgraph $S$ of $G$, let $alpha_S(G)$ be the maximum number of vertices in $G$ such that no two of them are in the same star subgraph $S$ and $theta_S(G)$ be the minimum number of star subgraph $S$ that cover the vertices of $G$. A graph $G$ is called $S$-perfect if for every induced subgraph $H$ of $G$, $alpha_S(H)=theta_S(H)$. Motivated by perfect graphs discovered by Berge, Ravindra introduced $S$-perfect graphs. In this paper we prove that a triangulated graph is $S$-perfect if and only if $G$ is odd sun-free. This result leads to a conjecture which if proved is a structural characterization of $S$-perfect graphs in terms of forbidden subgraphs." @default.
- W4375870085 created "2023-05-10" @default.
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- W4375870085 date "2023-05-05" @default.
- W4375870085 modified "2023-09-26" @default.
- W4375870085 title "Odd sun-free Triangulated Graphs are $S$-perfect" @default.
- W4375870085 doi "https://doi.org/10.48550/arxiv.2305.03540" @default.
- W4375870085 hasPublicationYear "2023" @default.
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