منابع مشابه
On the balanced decomposition number
A balanced coloring of a graph G means a triple {P1, P2,X} of mutually disjoint subsets of the vertex-set V (G) such that V (G) = P1⊎P2⊎X and |P1| = |P2|. A balanced decomposition associated with the balanced coloring V (G) = P1⊎P2⊎X of G is defined as a partition of V (G) = V1⊎· · ·⊎Vr (for some r) such that, for every i ∈ {1, · · · , r}, the subgraphG[Vi] of G is connected and |Vi∩P1| = |Vi∩P...
متن کاملFurther Results on the Balanced Decomposition Number
A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪̇ · · · ∪̇Vr such that, for every 1 ≤ i ≤ r, Vi induces a ...
متن کاملOn a conjecture on the balanced decomposition number
The concept of balanced decomposition number was introduced by Fujita and Nakamigawa in connection with a simultaneous transfer problem. A balanced colouring of a graph G is a pair (R,B) of disjoint subsets R,B ⊆ V (G) with |R| = |B|. A balanced decomposition D of a balanced colouring C = (R,B) of G is a partition of vertices V (G) = V1 ∪ V2 ∪ . . . ∪ Vr such that G[Vi] is connected and |Vi ∩R|...
متن کاملThe Balanced Decomposition Number and Vertex Connectivity
The balanced decomposition number f(G) of a graph G was introduced by Fujita and Nakamigawa [Discr. Appl. Math., 156 (2008), pp. 3339-3344]. A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, such that there is the same number of vertices in each colour. Then, f(G) is the minimum integer s with the following property: For any balanced colouring of G,...
متن کاملThe balanced decomposition number of TK4 and series -parallel graphs
A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪̇ · · · ∪̇Vr such that, for every i, Vi induces a connecte...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2015
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-015-1526-5