Vertex intersection graphs of paths on a grid: characterization within block graphs

LILIANA ALCÓN; FLAVIA BONOMO; MARÍA PÍA MAZZOLENI

GRAPHS AND COMBINATORICS

SPRINGER TOKYO

Lugar: Tokyo; Año: 2017 vol. 33 p. 653 - 664

0911-0119

We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called $B_0$-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time algorithm for recognizing chordal $B_0$-VPG graphs. In this paper, we present a minimal forbidden induced subgraph characterization of $B_0$-VPG graphs restricted to block graphs.  As a byproduct, the proof of the main theorem provides an alternative certifying recognition and representation algorithm for $B_0$-VPG graphs in the class of block graphs.