On Critically Perfect Graphs on Critically Perfect Graphs
نویسنده
چکیده
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.
منابع مشابه
ANNEGRET K . WAGLER Critical and Anticritical Edges with respect to Perfectness
We call an edge e of a perfect graph G critical if G e is imperfect and call e anticritical if G + e is imperfect. The present paper surveys several questions in this context. We ask in which perfect graphs critical and anticritical edges occur and how to detect such edges. The main result by Hougardy & Wagler [32] shows that a graph does not admit any critical edge if and only if it is Meyniel...
متن کاملOn the Eccentric Connectivity Index of Unicyclic Graphs
In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.
متن کاملOn critically k-extendable graphs
Let G be a simple connected graph on 2n vertices with a perfect matching. G is k-extendable if for any set M of k independent edges, there exists a perfect matching in G containing all the edges of M. G is critically k-extendable if G is k-extendable but G + uv is not k-extendable for any non-adjacent pair of vertices u and v of G. The problem that arises is that of characterizing k-extendable ...
متن کاملPerfect Matchings in Edge-Transitive Graphs
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...
متن کاملPerfect $2$-colorings of the Platonic graphs
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.
متن کامل