Results 31 to 40 of about 505,548 (331)
Theory and Applications of Graphs, 2022 Given an edge-colored complete graph Kn on n vertices, a perfect (respectively, near-perfect) matching M in Kn with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors.
Shuhei Saitoh, Naoki Matsumoto, Wei Wu
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Perfectness of clustered graphs [PDF]
Discrete Optimization, 2013 Given a clustered graph (G,V), that is, a graph G=(V,E) together with a partition V of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum.
Denis Cornaz +5 more
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On the number of perfect matchings in random polygonal chains
Open Mathematics, 2023 Let GG be a graph. A perfect matching of GG is a regular spanning subgraph of degree one. Enumeration of perfect matchings of a (molecule) graph is interest in chemistry, physics, and mathematics.
Wei Shouliu +3 more
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Systems with the integer rounding property in normal monomial subrings
Anais da Academia Brasileira de Ciências, 2010 Let C be a clutter and let A be its incidence matrix. If the linear system x > 0; x A < 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a
Luis A. Dupont +2 more
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Bounds on perfect k-domination in trees: an algorithmic approach [PDF]
Opuscula Mathematica, 2012 Let \(k\) be a positive integer and \(G = (V;E)\) be a graph. A vertex subset \(D\) of a graph \(G\) is called a perfect \(k\)-dominating set of \(G\) if every vertex \(v\) of \(G\) not in \(D\) is adjacent to exactly \(k\) vertices of \(D\). The minimum
B. Chaluvaraju, K. A. Vidya
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Perfection thickness of graphs
Discrete Mathematics, 2000 For a graph \(G\), let \(f(G)\) be the least number of perfect subgraphs of \(G\) whose union is \(G\). Let \(f(n)= \max\{f(G):|V(G)|= n\}\). Improving results of Zs. Tuza, the authors prove that \[ \textstyle{{1\over 2}}(\log n-\log\log n- O(1))\leq f(n)\leq \lceil\log n\rceil, \] where \(\log\) denotes the base-2 logarithm.
Tao Jiang +3 more
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Discrete Applied Mathematics, 2019 Inspired by a famous characterization of perfect graphs due to Lov sz, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $ (H) + (H) \geq |V(H)|$. (Here $ $ and $ $ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $
Bart Litjens +2 more
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Hitting time results for Maker-Breaker games [PDF]
, 2010 We study Maker-Breaker games played on the edge set of a random graph. Specifically, we consider the random graph process and analyze the first time in a typical random graph process that Maker starts having a winning strategy for his final graph to ...
Alon +24 more
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Perfect codes in power graphs of finite groups
Open Mathematics, 2017 The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong +4 more
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Perfect Outer-connected Domination in the Join and Corona of Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let 𝐺 be a connected simple graph. A dominating set 𝑆 ⊆ 𝑉(𝐺) is called a perfect dominating set of 𝐺 if each 𝑢 ∈ 𝑉 𝐺 ∖ 𝑆 is dominated by exactly one element of 𝑆.
Enrico Enriquez +3 more
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