Minimal forbidden induced subgraphs characterization of Block B0-VPG graphs

LILIANA ALCÓN; FLAVIA BONOMO; MARÍA PÍA MAZZOLENI

La Plata

Workshop; VII Latin-American Workshop on Cliques in Graphs -LAWCliques'2016; 2016

Universidad Nacional de La Plata

We investigate graphs that can be represented as vertex intersections of horizontal andvertical paths in a grid, the so called B0-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time algorithm for recognizing chordal B0-VPG graphs. In this paper, we present a minimal forbidden induced subgraph characterization of B0-VPG graphs restricted to block graphs. As a byproduct, the proof of the main theorem provides an alternative certifying recognition and representation algorithm for B0-VPG graphs in the class of block graphs.