منابع مشابه
A Correspondence Between Maximal Complete Bipartite Subgraphs and Closed Patterns
For an undirected graph without self-loop, we prove: (i) that the number of closed patterns in the adjacency matrix of is even; (ii) that the number of the closed patterns is precisely double the number of maximal complete bipartite subgraphs of ; (iii) that for every maximal complete bipartite subgraph, there always exists a unique and distinct pair of closed patterns that matches the two vert...
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Santa likes to run a lean and efficient toy-making operation. He also likes to keep up with the latest math developments. So naturally, when Santa was building a new factory a few years back, he designed an interesting factory and method for assigning workers to toys that was based on a recent article he read in the Monthly ??. Here were some of Santa’s constraints. As it turns out, each toy re...
متن کاملComplete subgraphs in multipartite graphs
Turán’s Theorem states that every graphG of edge density ‖G‖/ (|G| 2 ) > k−2 k−1 contains a complete graph K and describes the unique extremal graphs. We give a similar Theorem for `-partite graphs. For large `, we find the minimal edge density d` , such that every `-partite graph whose parts have pairwise edge density greater than d` contains a K . It turns out that d` = k−2 k−1 for large enou...
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Define a complete subgraph Q to be simplicial in a graph G when Q is contained in exactly one maximal complete subgraph (‘maxclique’) of G; otherwise, Q is nonsimplicial. Several graph classes—including strong p-Helly graphs and strongly chordal graphs—are shown to have pairs of peculiarly related new characterizations: (i) for every k ≥ 2, a certain property holds for the complete subgraphs th...
متن کاملComplete subgraphs of random graphs
A classical theorem by Erdős, Kleitman and Rothschild on the structure of triangle-free graphs states that with high probability such graphs are bipartite. Our first main result refines this theorem by investigating the structure of the ’few’ triangle-free graphs which are not bipartite. We prove that with high probability these graphs are bipartite up to a few vertices. Similar results hold if...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1972
ISSN: 0095-8956
DOI: 10.1016/0095-8956(72)90038-x