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Proceedings of the London Mathematical Society, 2020 We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the resulting set is ...
Grzesik, Andrzej +2 more
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Tight upper bound on the maximum anti-forcing numbers of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed that the maximum anti-forcing number of $G$ is no more than the cyclomatic number.
Lingjuan Shi, Heping Zhang
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Extremal Optimization for Graph Partitioning [PDF]
Physical Review E, 2001 Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem.
A. K. Hartmann +44 more
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On some interconnections between combinatorial optimization and extremal graph theory [PDF]
Yugoslav Journal of Operations Research, 2004 The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set.
Cvetković Dragoš M. +2 more
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Capture-Time Extremal Cop-Win Graphs
Discussiones Mathematicae Graph Theory, 2021 We investigate extremal graphs related to the game of Cops and Robbers. We focus on graphs where a single cop can catch the robber; such graphs are called cop-win.
Offner David, Ojakian Kerry
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The Signless Laplacian Estrada Index of Unicyclic Graphs [PDF]
Mathematics Interdisciplinary Research, 2017 For a simple graph G, the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi, where q1, q2,..., qn are the eigenvalues of the signless Laplacian matrix of G.
Hamid Reza Ellahi +3 more
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On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs
Frontiers in Physics, 2020 With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory.
Hongyan Lu, Zhongxun Zhu
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A note on the Ramsey numbers for theta graphs versus the wheel of order 5
AKCE International Journal of Graphs and Combinatorics, 2018 The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat +3 more
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Construction Algorithm of Given Girth Graphs Based on Quantum Evolution [PDF]
Jisuanji gongcheng, 2017 To construct an extremal graph with a given girth is still a challenging problem of graph theory.Especially when the vertex number increasex combination explosion will appear.Thus,this paper proposes an algorithm for constructing graphs with given girth ...
FENG Xiaohua,SUN Yongqi
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Ars Mathematica Contemporanea, 2019 Summary: Let \(G\) be a ribbon graph and \(\mu (G)\) be the number of components of the virtual link formed from \(G\) as a cellularly embedded graph via the medial construction. In this paper we first prove that \(\mu (G) \leq f(G) + \gamma (G)\), where \(f(G)\) and \(\gamma (G)\) are the number of boundary components and Euler genus of \(G ...
Jin, Xian'an, Yan, Qi
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