The existence of homeomorphic subgraphs in chordal graphs Original Research Article

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to Kn (n ≥ 3), Km,n (m, n ≥ 2), and wheels Wr (r ≥ 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some special classes of pattern graphs.