Characterization of Cycle Obstruction Sets for Improper Coloring Planar Graphs Academic Article uri icon

abstract

  • 2018 Society for Industrial and Applied Mathematics. For nonnegative integers k, d1, . . ., dk, a graph is (d1, . . ., dk)-colorable if its vertex set can be partitioned into k parts so that the ith part induces a graph with maximum degree at most di for all i {1, . . ., k}. A class C of graphs is balanced k-partitionable and unbalanced k-partitionable if there exists a nonnegative integer D such that all graphs in C are (D, . . ., D)colorable and (0, . . ., 0, D)-colorable, respectively, where the tuple has length k. A set X of cycles is a cycle obstruction set of a class C of planar graphs if every planar graph containing none of the cycles in X as a subgraph belongs to C. This paper characterizes all cycle obstruction sets of planar graphs to be balanced k-partitionable and unbalanced k-partitionable for all k; namely, we identify all inclusionwise minimal cycle obstruction sets for all k.

published proceedings

  • SIAM Journal on Discrete Mathematics

author list (cited authors)

  • Choi, I., Liu, C., & Oum, S.

publication date

  • January 1, 2018 11:11 AM