For two integers a and b, we say that a bipartite graph G admits an (a, b)bipartition if G has a bipartition (X, Y ) such that |X| = a and |Y | = b. We say that two bipartite graphs G and H are compatible if, for some integers a and b, both G and H admit (a, b)-bipartitions. In this paper, we prove
Packing smaller graphs into a graph
β Scribed by Jin Akiyama; Fumi Nakada; Sinichi Tokunaga
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 117 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Let G be a graph. Given an integer m < IV(G)l, we obtain a lower bound for the largest number of vertex-disjoint subgraphs of G, each of which has m vertices.
π SIMILAR VOLUMES
## Abstract In this study, we provide methods for drawing a tree with __n__ vertices on a convex polygon, without crossings and using the minimum number of edges of the polygon. We apply the results to obtain planar packings of two trees in some specific cases. Β© 2002 Wiley Periodicals, Inc. J Grap
For two integers a and b, we say that a bipartite graph G admits an ( a , b)-bipartition if G has a bipartition ( X , Y ) such that /XI = a and ( Y / = b. We say that two bipartite graphs G and H are compatible if, for some integers a and b, both G and H admit ( a , b)-bipartitions. In this note, w
Let IGI be the number of vertices of a graph G and to(G) be the density of G. We call a graph G packed if the clique graph K(G) of G has exactly 2 IGI-O'(G) cliques. We correct the characterization of clique graphs of packed graphs given in Theorem 3.2 of Hedman [3]. All graphs considered here are f
## Abstract We show that if a tree __T__ is not a star, then there is an embedding Ο of __T__ in the complement of __T__ such that the maximum degree of __T__βͺΟ(__T__) is at most Ξ(__T__)+2. We also show that if __G__ is a graph of order __n__ with __n__β1 edges, then with several exceptions, there
We verify that the Tree Packing Conjecture is true for all sequences of trees T 1 , . . . , T n such that there exists x i β V (T i ) and T i -x i has at least i -6(i -1)/4 isolated vertices.