A graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths inG such that every path in ψ has at least two vertices, every vertex ofG is an internal vertex of at most one path in ψ and every edge of G is in exactly one path in ψ. Let Ω (ψ) denote the intersection graph of ψ. A graph G is said to be graphoidal if there exists a graphH and a graphoidal cover ψof H such that G is isomorphic to Ω(ψ). In this paper we study the properties of graphoidal graphs and obtain a forbidden subgraph characterisation of bipartite graphoidal graphs.
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Arumugam, S., Pakkiam, C. Graphoidal bipartite graphs. Graphs and Combinatorics 10, 305–310 (1994). https://doi.org/10.1007/BF02986680
- Bipartite Graph
- Intersection Graph
- Complete Bipartite Graph
- Internal Vertex
- Terminal Vertex