Characterization of general position sets and its applications to cographs and bipartite graphs

Bijo S. Anand, Ullas Chandran S. V., Manoj Changat, Sandi Klavžar and Elias John Thomas

Applied Mathematics and Computation, 2019, vol. 359, issue C, 84-89

Abstract: A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number gp(G) of G. It is proved that S⊆V(G) is in general position if and only if the components of G[S] are complete subgraphs, the vertices of which form an in-transitive, distance-constant partition of S. If diam(G)=2, then gp(G) is the maximum of ω(G) and the maximum order of an induced complete multipartite subgraph of the complement of G. As a consequence, gp(G) of a cograph G can be determined in polynomial time. If G is bipartite, then gp(G) ≤ α(G) with equality if diam(G) ∈ {2, 3}. A formula for the general position number of the complement of an arbitrary bipartite graph is deduced and simplified for the complements of trees, of grids, and of hypercubes.

Keywords: General position set; Graph of diameter 2; Cograph; Bipartite graph; Bipartite complement (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:359:y:2019:i:c:p:84-89

DOI: 10.1016/j.amc.2019.04.064

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