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Some classes of non-induced star-perfect graphs | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 خرداد 1404 اصل مقاله (776.33 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2025.29860.2196 | ||
نویسندگان | ||
James Alex* ؛ Louis Caccetta | ||
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Australia | ||
چکیده | ||
For a given graph $G$, let $\theta_f(G)$ denote the minimum number of stars (not necessarily induced) needed to cover the vertices of $G$, and let $\alpha_f(G)$ denote the maximum number of vertices in a set $S \subseteq V(G)$ such that no two distinct vertices $u, v \in S$ belong to the same subgraph of $G$ that is a star. Clearly, $\theta_f(G) \geq \alpha_f(G)$. A graph $G$ is said to be \emph{non-induced star-perfect} if $\theta_f(H) = \alpha_f(H)$ for every induced subgraph $H$ of $G$. A graph $G$ is a \emph{domination graph} if every induced subgraph $H$ of $G$ contains a pair of vertices $x, y$ such that $N_H(x) \subseteq N_H[y]$. In this paper, we investigate domination graphs that are non-induced star-perfect and explore well-known subclasses within this category. Additionally, we present an integer linear programming formulation that characterizes a polytope associated with the star-covering set and star-independence set of a graph. | ||
کلیدواژهها | ||
Star-perfect؛ star-covering number؛ star-independence number؛ chordal graphs؛ domination graphs | ||
مراجع | ||
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