The existence of homeomorphic subgraphs in chordal graphs
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TL;DR: In this paper, the authors established conditions for the existence of subgraphs homeomorphic to K n (n ≥ 3), K m, n (m, n ≥ 2), and wheels W r (r ≥ 3).
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About: This article is published in Applied Mathematics Letters. The article was published on 01 May 1997. and is currently open access. The article focuses on the topics: Chordal graph & Indifference graph.
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Citations
One-phase algorithm for the determination of minimal vertex separators of chordal graphs
TL;DR: A new one-phase algorithm based on properties of the lexicographic breadth-first search is proposed and a characterization for planar chordal graphs is presented; using the proposed algorithm as an initial step, the implementation of the recognition algorithm becomes trivial.
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Structure and Recognition of Graphs with No 6-wheel Subdivision
Rebecca Robinson,Graham Farr +1 more
TL;DR: The main result is a theorem characterizing graphs that do not contain subdivisions of W6, an efficient algorithm for solving the subgraph homeomorphism problem for W6 and a strengthening of the previous W5 result.
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Efficient Planarity Testing
TL;DR: An efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane is described, which used depth-first search and has time and space bounds.
Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs
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