Locally perfect graphs
نویسندگان
چکیده
منابع مشابه
Measurable Perfect Matchings for Acyclic Locally Countable Borel graphs
We characterize the structural impediments to the existence of Borel perfect matchings for acyclic locally countable Borel graphs admitting a Borel selection of finitely many ends from their connected components. In particular, this yields the existence of Borel matchings for such graphs of degree at least three. As a corollary, it follows that acyclic locally countable Borel graphs of degree a...
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In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
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We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
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A (proper) coloring of a finite simple graph (G) is pe#ect if it uses exactly o(G) colors, where o(G) denotes the order of a largest clique in G. A coloring is locally-perfect [3] if it induces on the neighborhood of every vertex v a perfect coloring of this neighborhood. A graph G is perfect (resp. locally-petfect) if every induced subgraph admits a perfect (resp. locally-perfect) coloring. Pr...
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A perfect graph is critical if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We relate critically perfect graphs to well-known classes of perfect graphs, investigate the structure of the class of critically perfect graphs, and study operations preserving critical perfectness.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1990
ISSN: 0095-8956
DOI: 10.1016/0095-8956(90)90094-g