Netlike partial cubes II. Retracts and netlike subgraphs |
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Authors: | Norbert Polat |
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Affiliation: | I.A.E., Université Jean Moulin (Lyon 3), 6 cours Albert Thomas, 69355 Lyon Cedex 08, France |
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Abstract: | First we show that the class of netlike partial cubes is closed under retracts. Then we prove, for a subgraph G of a netlike partial cube H, the equivalence of the assertions: G is a netlike subgraph of H; G is a hom-retract of H; G is a retract of H. Finally we show that a non-trivial netlike partial cube G, which is a retract of some bipartite graph H, is also a hom-retract of H if and only if G contains at most one convex cycle of length greater than 4. |
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Keywords: | Netlike partial cube Netlike subgraph Retract Hom-retract Prism-retractable graph |
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