Results 21 to 30 of about 505,548 (331)
Random Structures & Algorithms, 2018 We investigate the asymptotic structure of a random perfect graph Pn sampled uniformly from the set of perfect graphs on vertex set . Our approach is based on the result of Prömel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.
McDiarmid, C, Yolov, N
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AKCE International Journal of Graphs and Combinatorics, 2020 A graph of order is domatically perfect if , where and denote the domination number and the domatic number, respectively. In this paper, we give basic results for domatically perfect graphs, and study a main problem; for a given graph , to find a ...
Naoki Matsumoto
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Parameterized Algorithms on Perfect Graphs for deletion to $(r,\ell)$-graphs [PDF]
, 2015 For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. The class of $(r, \ell)$ graphs generalizes $r$-colourable graphs (when $\ell =0)
Kolay, Sudeshna +3 more
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Discrete Mathematics, 1986 Let G be a graph. The authors denote by \(\alpha_ N(G)\) the maximum number of edges of G such that no two of them belong to the same neighborhood subgraph of G (that is a subgraph induced by a vertex v and the vertices adjacent to v). They denote by \(\rho_ N(G)\) the minimum number of vertices whose neighborhood subgraphs cover the edge set of G.
Zs. Tuza, Jenö Lehel
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Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs
Journal of Chemistry, 2021 A connected graph GV,E in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set ...
Muhammad Rizwan +3 more
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Fractional matching preclusion for butterfly derived networks
Theory and Applications of Graphs, 2019 The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings.
Xia Wang +4 more
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The 2-Factor Polynomial Detects Even Perfect Matchings [PDF]
, 2020 In this paper, we prove that the 2-factor polynomial, an invariant of a planar trivalent graph with a perfect matching, counts the number of 2- factors that contain the the perfect matching as a subgraph. Consequently, we show that the polynomial detects
Baldridge, Scott +2 more
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Commuting decomposition of Kn1,n2,...,nk through realization of the product A(G)A(GPk )
Special Matrices, 2018 In this paper, we introduce the notion of perfect matching property for a k-partition of vertex set of given graph. We consider nontrivial graphs G and GPk , the k-complement of graph G with respect to a kpartition of V(G), to prove that A(G)A(GPk ) is ...
Bhat K. Arathi, Sudhakara G.
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Formation of Non-Perfect Maze Using Prim’s Algorithm
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 Maze is a place that has many paths with tortuous paths that are misleading and full of dead ends and can be viewed as a grid graph. A non-perfect maze is a maze that has a cycle.
Mahyus Ihsan +4 more
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On kernels in strongly game-perfect digraphs and a characterisation of weakly game-perfect digraphs
AKCE International Journal of Graphs and Combinatorics, 2020 We prove that the game-perfect digraphs defined by Andres (2012) with regard to a digraph version of the maker-breaker graph colouring game introduced by Bodlaender (1991) always have a kernel.
Stephan Dominique Andres
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