In this paper, we introduce a graph operation, namely one-three join. We show that the graph G admits a one-three join if and only if either G is one of the basic graphs (bipartite, complement of bipartite, split graph) or G admits a constrained homogeneous set or a bipartite-join or a join. Next, we define ℳH as the class of all graphs generated from the induced subgraphs of an odd hole-free graph H that contains an odd anti-hole as an induced subgraph by using one-three join and co-join recursively and show that the maximum independent set problem, the maximum clique problem, the minimum coloring problem, and the minimum clique cover problem can be solved efficiently for ℳH.
@article{bwmeta1.element.doi-10_7151_dmgt_1948,
author = {M.A. Shalu and S. Devi Yamini},
title = {One-Three Join: A Graph Operation and Its Consequences},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {633-647},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1948}
}
M.A. Shalu; S. Devi Yamini. One-Three Join: A Graph Operation and Its Consequences. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 633-647. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1948/