Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs

Abstract

It follows from the work of Tait and the Four-Color-Theorem that a planar cubic graph is 3-edgecolorable if and only if it contains no bridge. We consider the question of which planar graphs are subgraphs of planar cubic bridgeless graphs, and hence 3-edge-colorable. We provide an efficient recognition algorithm that given an n-vertex planar graph, augments this graph in O(n 2 ) steps to a planar cubic bridgeless supergraph, or decides that no such augmentation is possible. The main tools involve the Generalized Factor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case. ACM Subject ClassificationTheory of computation → Design and analysis of algorithms → Graph algorithms analysis