Results 31 to 40 of about 34,455 (233)
The existence of subdigraphs with orthogonal factorizations in digraphs
AIMS Mathematics, 2021 Let $G$ be a $[0,k_1+k_2+\cdots+k_m-n+1]$-digraph and $H_1,H_2,\cdots,H_r$ be $r$ vertex-disjoint $n$-subdigraphs of $G$, where $m,n,r$ and $k_i$ ($1\leq i\leq m$) are positive integers satisfying $1\leq n\leq m$ and $k_1\geq k_2\geq\cdots\geq k_m\geq r ...
Sizhong Zhou, Quanru Pan
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Journal of Combinatorial Theory, Series B, 1993 We introduce a generalization of digraphs that are local tournaments. This is the class of in-tournament digraphs---the set of predecessors of every vertex induces a tournament. We show that many properties of local tournament digraphs can be extended even to in-tournament digraphs.
Erich Prisner +2 more
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Computers & Mathematics with Applications, 1997 The authors recall known results concerning distance in a graph and standard distance in a digraph. They define two new distances in strong digraphs: \(d_{\max} (u,v)= \max (d(u,v),\;d(v,u))\) and \(d_{\text{sum}} (u,v)= d(u,v) +d(v,u)\). Several results and problems concerning these distances and parameters such as center, median, and periphery are ...
Gary Chartrand, S. Tian
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Kernels by Monochromatic Paths and Color-Perfect Digraphs
Discussiones Mathematicae Graph Theory, 2016 For a digraph D, V (D) and A(D) will denote the sets of vertices and arcs of D respectively. In an arc-colored digraph, a subset K of V(D) is said to be kernel by monochromatic paths (mp-kernel) if (1) for any two different vertices x, y in N there is no
Galeana-Śanchez Hortensia +1 more
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Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code
Discussiones Mathematicae Graph Theory, 2021 A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph
Balbuena Camino +2 more
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Out-degree reducing partitions of digraphs [PDF]
, 2017 Let $k$ be a fixed integer. We determine the complexity of finding a $p$-partition $(V_1, \dots, V_p)$ of the vertex set of a given digraph such that the maximum out-degree of each of the digraphs induced by $V_i$, ($1\leq i\leq p$) is at least $k ...
Bang-Jensen, Joergen +3 more
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Are there any good digraph width measures? [PDF]
, 2010 Several different measures for digraph width have appeared in the last few years. However, none of them shares all the "nice" properties of treewidth: First, being \emph{algorithmically useful} i.e.
B. Courcelle +15 more
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On the Capacity of Digraphs [PDF]
European Journal of Combinatorics, 1998 For a digraph \(G= (V,E)\) let \(\omega(G^n)\) denote the maximum possible cardinality of a subset \(S\) of \(V^n\) in which for every ordered pair of \(n\)-tuples \((u_1, u_2,\dots, u_n)\) and \((v_1, v_2,\dots, v_n)\) of members of \(S\) there is some \(i\) with \(1\leq i\leq n\) such that \((u_i,v_i)\in E\). The capacity \(C(G)\) of \(G\) is \(C(G)=
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Some Results on 4-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2017 Let D be a digraph with set of vertices V and set of arcs A. We say that D is k-transitive if for every pair of vertices u, v ∈ V, the existence of a uv-path of length k in D implies that (u, v) ∈ A.
García-Vázquez Patricio Ricardo +1 more
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Graph partitioning: an updated survey
AKCE International Journal of Graphs and Combinatorics, 2023 Graph partitioning problem, which is one of the most important topics in graph theory, usually asks for a partition of the vertex set of a graph into pairwise disjoint subsets with various requirements. It comes from the well-known Max-Cut Problem: Given
Shufei Wu, Jianfeng Hou
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