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Some properties of star-perfect graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 11، شماره 1، خرداد 2026، صفحه 49-56 اصل مقاله (640.74 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28076.1484 | ||
| نویسندگان | ||
| Sanghita Ghosh* ؛ Ravindra Gundgurti؛ Abraham Vettiyankal | ||
| Department of Mathematics, CHRIST(Deemed to be University), Bengaluru, India | ||
| چکیده | ||
| For a finite simple graph $G=(V, E)$, $\theta_s(G)$ denotes the minimum number of induced stars contained in $G$ such that the union of their vertex sets is $V(G)$, and $ \alpha_s(G)$ denotes the maximum number of vertices in $G$ such that no two are contained in the same induced star of $G$. We call the graph $G$ star-perfect if $\alpha_s(H)=\theta_s(H)$, for every induced subgraph $H$ of $G$. We prove here that no cycle in a star-perfect graph has crossing chords and star-perfect graphs are planar. Also we present a few properties of star perfect graphs. | ||
| کلیدواژهها | ||
| star-perfect graphs؛ crossing chords؛ planar graph؛ total graphs | ||
| مراجع | ||
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[7] G. Ravindra, S. Ghosh, and V. M. Abraham, Some results on star-perfect graphs, (submitted).
[8] G. Ravindra, S. Ghosh, J.V. Kureethara, and V.M. Abraham, A characterisation of star-perfect graphs, AKCE Int. J. Graphs Comb. 21 (2024), no. 2, 189–197. https://doi.org/10.1080/09728600.2024.2329927
[9] D.B. West, Introduction to Graph Theory, Prentice hall Upper Saddle River, USA, 2001. | ||
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