منابع مشابه
Acyclic dominating partitions
Given a graph G = (V,E), let P be a partition of V . We say that P is dominating if, for each part P of P, the set V \ P is a dominating set in G (equivalently, if every vertex has a neighbour of a different colour from its own). We say that P is acyclic if for any parts P, P ′ of P, the bipartite subgraph G[P, P ′] consisting of the edges between P and P ′ in P contains no cycles. The acyclic ...
متن کاملMinimal dominating sets in maximum domatic partitions
The domatic number d(G) of a graph G = (V,E) is the maximum order of a partition of V into dominating sets. Such a partition Π = {D1, D2, . . . , Dd} is called a minimal dominating d-partition if Π contains the maximum number of minimal dominating sets, where the maximum is taken over all d-partitions of G. The minimal dominating d-partition number Λ(G) is the number of minimal dominating sets ...
متن کاملk-Colour Partitions of Acyclic Tournaments
Let G1 be the acyclic tournament with the topological sort 0 < 1 < 2 < · · · < n < n + 1 defined on node set N ∪ {0, n + 1}, where N = {1, 2, . . . , n}. For integer k ≥ 2, let Gk be the graph obtained by taking k copies of every arc in G1 and colouring every copy with one of k different colours. A k-colour partition of N is a set of k paths from 0 to n + 1 such that all arcs of each path have ...
متن کاملOn H-dominating matchings and some number partitions
A dominating set of a graph G = (V,E) is a subset D of V such that every vertex of V − D is adjacent to a vertex in D. In this paper we introduce a generalization of domination as follows. For graphs G and H, an H-matching M of G is a subgraph of G such that all components of M are isomorphic to H. An H-dominating matching of G is a Hmatching D of G such that for each x ∈ V (G) there exists y ∈...
متن کاملIndependent Dominating Sets and Idomatic Partitions in Direct Products of Four Complete Graphs
Independent dominating sets in the direct product of four complete graphs are considered. Possible types of such sets are classified. The sets in which every pair of vertices agree in exactly one coordinate, called T1-sets, are explicitly described. It is proved that the direct product of four complete graphs admits a partition into T1-sets if and only if each factor has at least three vertices...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2007
ISSN: 1571-0653
DOI: 10.1016/j.endm.2007.07.068