منابع مشابه
Saturation Numbers in Tripartite Graphs
Given graphs H and F , a subgraph G ⊆ H is an F -saturated subgraph of H if F * G, but F ⊆ G + e for all e ∈ E(H) \ E(G). The saturation number of F in H, denoted sat(H,F ), is the minimum number of edges in an F -saturated subgraph of H. In this paper we study saturation numbers of tripartite graphs in tripartite graphs. For ` ≥ 1 and n1, n2, and n3 sufficiently large, we determine sat(Kn1,n2,...
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We present a piecewise formula for the competition numbers of the complete tripartite graphs. For positive integers x, y and z where 2 ≤ x ≤ y ≤ z, the competition number of the complete tripartite graph Kx,y,z is yz − z − y − x + 3 whenever x 6= y and yz − 2y − z + 4 otherwise.
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For a graph G, it is known to be a hard problem to compute the competition number k(G) of the graph G in general. In this paper, we give an explicit formula for the competition numbers of complete tripartite graphs.
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An upper bound on the saturation number for graphs as well as associated extremal graphs was given by (Kászonyi and Tuza in J. Graph Theory, 10:203–210, 1986). A minor improvement of that result, which was implied in their paper, will be stated. Using this result, a series of exact saturation numbers and associated extremal graphs will be proved for the nearly complete graphs Kt − E(L), where L...
متن کاملWeak saturation numbers for sparse graphs
For a fixed graph F , a graph G is F -saturated if there is no copy of F in G, but for any edge e 6∈ G, there is a copy of F in G+ e. The minimum number of edges in an F -saturated graph of order n will be denoted by sat(n, F ). A graph G is weakly F -saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F . Th...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2016
ISSN: 0364-9024
DOI: 10.1002/jgt.22033