منابع مشابه
The Saturation Function of Complete Partite Graphs
A graph G is called F -saturated if it is F -free but the addition of any missing edge to G creates a copy of F . Let the saturation function sat(n, F ) be the minimum number of edges that an F -saturated graph on n vertices can have. We determine this function asymptotically for every fixed complete partite graph F as n tends to infinity and give some structural information about almost extrem...
متن کاملExtremal Problems for t-Partite and t-Colorable Hypergraphs
Fix integers t ≥ r ≥ 2 and an r-uniform hypergraph F . We prove that the maximum number of edges in a t-partite r-uniform hypergraph on n vertices that contains no copy of F is ct,F ( n r ) + o(nr), where ct,F can be determined by a finite computation. We explicitly define a sequence F1, F2, . . . of r-uniform hypergraphs, and prove that the maximum number of edges in a t-chromatic r-uniform hy...
متن کاملOn Edge-Colored Saturation Problems
Let C be a family of edge-colored graphs. A t-edge colored graph G is (C, t)saturated if G does not contain any graph in C but the addition of any edge in any color in [t] creates a copy of some graph in C. Similarly to classical saturation functions, define satt(n, C) to be the minimum number of edges in a (C, t) saturated graph. Let Cr(H) be the family consisting of every edge-colored copy of...
متن کاملExact bounds for some hypergraph saturation problems
Let Wn(p, q) denote the minimum number of edges in an n× n bipartite graph G on vertex sets X,Y that satisfies the following condition; one can add the edges between X and Y that do not belong to G one after the other so that whenever a new edge is added, a new copy of Kp,q is created. The problem of bounding Wn(p, q), and its natural hypergraph generalization, was introduced by Balogh, Bollobá...
متن کاملCertain t-partite graphs
By making use of the generalized concept of orthogonality in Latin squares, certain t-partite graphs have been constructed and a suggestion for a net work system has been made.
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2016
ISSN: 0364-9024
DOI: 10.1002/jgt.22071