Clique-width and induced topological minors
Abstract
A P4 is a chordless path on four vertices. A diamond is a graph obtained from a clique of size four by removing one edge of the clique. A paw is a graph obtained from a clique of size four by removing two adjacent edges of the clique. We prove that for a graph H, the class of graphs with no induced subdivision of H has bounded clique-width if and only if H is an induced subgraph of P4, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma.
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