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Extremal graphs for homomorphisms [PDF]
Journal of Graph Theory, 2011 Summary: The study of graph homomorphisms has a long and distinguished history, with applications in many areas of graph theory. There has been recent interest in counting homomorphisms, and in particular on the question of finding upper bounds for the number of homomorphisms from a graph \(G\) into a fixed image graph \(H\).
Jonathan Cutler
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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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Extremal Graphs for Homomorphisms II
Journal of Graph Theory, 2013AbstractExtremal 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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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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Characterizations of Strength Extremal Graphs
Graphs and Combinatorics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaofeng Gu 0002 +3 more
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Extremal graphs for the odd prism
Discrete MathematicsThe Turán number $\mathrm{ex}(n,H)$ of a graph $H$ is the maximum number of edges in an $n$-vertex graph which does not contain $H$ as a subgraph. The Turán number of regular polyhedrons was widely studied in a series of works due to Simonovits. In this paper, we shall present the exact Turán number of the prism $C_{2k+1}^{\square} $, which is defined ...
Lihua Feng, Xiaocong He
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Ars Comb., 1998
The authors consider the graph weight \(w_\alpha (G)=\sum _{e\in E(G)}w_{\alpha }(e)\), where \(\alpha \neq 0\) is fixed and \(w_{\alpha }(e)=w_{\alpha }(\{x,y\})=(d(x)d(y))^\alpha \) with \(d(x)\) being the degree of \(x\). It is proved that for the Randić weight \(\alpha =-1/2\) (in the first definition in the article the ``\(-\)'' is missing), if ...
Béla Bollobás, Paul Erdös
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The authors consider the graph weight \(w_\alpha (G)=\sum _{e\in E(G)}w_{\alpha }(e)\), where \(\alpha \neq 0\) is fixed and \(w_{\alpha }(e)=w_{\alpha }(\{x,y\})=(d(x)d(y))^\alpha \) with \(d(x)\) being the degree of \(x\). It is proved that for the Randić weight \(\alpha =-1/2\) (in the first definition in the article the ``\(-\)'' is missing), if ...
Béla Bollobás, Paul Erdös
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