The pagenumber p(G) of a graph G is defined as the smallest n such that G can be embedded in a book with n pages. We give an upper bound for the pagenumber of the complete bipartite graph K m, n . Among other things, we prove p(K n, n ) w2nร3x+1 and p(K wn 2 ร4x, n ) n&1. We also give an asymptotic
Pagenumber of complete bipartite graphs
โ Scribed by Douglas J. Muder; Margaret Lefevre Weaver; Douglas B. West
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 929 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
For a complete bipartite graph, the number of dependent edges in an acyclic orientation can be any integer from n-1 to e, where n and e are the number of vertices and edges in the graph. ## Ke3,words: Bipartite graph; Acyclic orientation Ill combinatorics we often ask whether an integer parameter
## Abstract Given a graph __G__, for each ฯ โ__V__(__G__) let __L__(ฯ ) be a list assignment to __G__. The wellโknown choice number __c__(__G__) is the least integer __j__ such that if |__L__(ฯ )| โฅ__j__ for all ฯ โ__V__(__G__), then __G__ has a proper vertex colouring ฯ with ฯ(ฯ ) โ __L__ (ฯ ) (โฯ โ__
P,-factorization of K,,,, is (i) m + n -0 (mod 3), (ii) m < 2n, (iii) n s 2m and (iv) 3mn/2(m + n) is an integer.
## Abstract A __rooted graph__ is a pair (__G, x__) where __G__ is a simple undirected graph and __x__ ฯต __V__(__G__). If __G__ if rooted at __x__, then its __rotation number h(G, x)__ is teh minimum number of edges in a graph __F__, of the same order as __G__, such that for all __v__ ฯต __V(F)__ we