crossing chords; planar graph; star-perfect graphs; total graphs
For a finite simple graph G = (V, E), ?s(G) denotes the minimum number of induced stars contained in G such that the union of their vertex sets is V (G), and ?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 ?s(H) = ?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. 2026 Azarbaijan Shahid Madani University.
Ghosh, Sanghita; Gundgurti, Ravindra; Vettiyankal, Abraham
Communications in Combinatorics and Optimization;Volume;11;Issue;1;pp.49-56
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https://doi.org/10.22049/cco.2023.28076.1484 https://www.scopus.com/pages/publications/105019802895?origin=resultslist
Ghosh S., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Gundgurti R., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Vettiyankal A., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India