Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10151208 | Discrete Applied Mathematics | 2018 | 15 Pages |
Abstract
In this paper, we show that Ï(G) is always at least as large as the asteroidal number of G, and equal to the asteroidal number of G when G is a connected distance hereditary graph that is not a clique. This implies that the classes of distance hereditary permutation graphs and distance hereditary AT-free graphs are the same, and we give a forbidden subgraph characterization of that class. We also establish the following upper bounds: Ï(G) is at most the clique cover number of G if G is not a clique, at most 1 plus the independence number of G, and at most ânâ2â where nâ¥3 is the number of vertices of G. Our results lead to linear time algorithms for finding the minimum number of corners that must be added to a given circle representation to produce a polygon representation, and for finding the asteroidal number of a distance hereditary graph, both of which are improvements over previous algorithms for those problems.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Lorna Stewart, Richard Valenzano,