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Constrained Representations of Map Graphs and Half-Squares

2019
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International Symposium on Mathematical Foundations of Computer Science
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The square of a graph H, denoted H 2 , is obtained from H by adding new edges between two distinct vertices whenever their distance in H is two. The half-squares of a bipartite graph B = (X, Y, EB) are the subgraphs of B 2 induced by the color classes X and Y , B 2 [X] and While Chen, Grigni, Papadimitriou proved that any map graph G = (V, EG) has a witness with at most 3|V | − 6 points, we show that, given a map graph G and an integer k, deciding if G admits a witness with at most k points is

doi:10.4230/lipics.mfcs.2019.13
dblp:conf/mfcs/LeL19
fatcat:lyte7e2k7rhc5pfgfqfdmkz7py