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Extremal Graphs for Homomorphisms II
Journal of Graph Theory, 2013 AbstractExtremal problems for graph homomorphisms have recently become a topic of much research. Let denote the number of homomorphisms from G to H. A natural set of problems arises when we fix an image graph H and determine which graph(s) G on n vertices and m edges maximize .
Jonathan Cutler, A. J. Radcliffe
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An extremal graph with given bandwidth
Theoretical Computer Science, 2007 The graph bandwidth problem is a well-known NP-complete problem. The relation between size of a graph and bandwidth is very interesting. The minimum size required in G with bandwidth B is denoted as m(n,B) while the graph G of order n and bandwidth B ...
Yung-Ling Lai
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Extremal graph theory and finite forcibility [PDF]
Electronic Notes in Discrete Mathematics, 2017 We study the uniqueness of optimal solutions to extremal graph theory problems. Our main result is a counterexample to the following conjecture of Lov´asz, which is often referred to as saying that “every extremal graph theory problem has a finitely ...
Andrzej Grzesik +1 more
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Czechoslovak Mathematical Journal, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chartrand, Gary, Zhang, Ping
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chartrand, Gary, Zhang, Ping
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Discrete Mathematics, Algorithms and Applications, 2012
For a connected graph G of order p ≥ 2 and a set W ⊆ V(G), a tree T contained in G is a Steiner tree with respect to W if T is a tree of minimum order with W ⊆ V(T). The set S(W) consists of all vertices in G that lie on some Steiner tree with respect to W. The set W is a Steiner set for G if S(W) = V(G).
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For a connected graph G of order p ≥ 2 and a set W ⊆ V(G), a tree T contained in G is a Steiner tree with respect to W if T is a tree of minimum order with W ⊆ V(T). The set S(W) consists of all vertices in G that lie on some Steiner tree with respect to W. The set W is a Steiner set for G if S(W) = V(G).
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Star Extremal Circulant Graphs
SIAM Journal on Discrete Mathematics, 1999A graph is said to be star extremal if its fractional chromatic number is equal to its circular chromatic number. In this paper, it is proven that some families of circulant graphs are star extremal. The results generalize some earlier results obtained by \textit{A. F. Sidorenko} [Discrete Math.
Ko-Wei Lih +2 more
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Extremal subgraphs of random graphs
Random Structures & Algorithms, 2012AbstractWe prove that there is a constant c > 0, such that whenever p ≥ n‐c, with probability tending to 1 when n goes to infinity, every maximum triangle‐free subgraph of the random graph Gn,p is bipartite. This answers a question of Babai, Simonovits and Spencer (Babai et al., J Graph Theory 14 (1990) 599–622).
Brightwell, G. +2 more
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Journal of Graph Theory, 1993
AbstractAn interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs.
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AbstractAn interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs.
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