P Γ³sa proved that if G is an n-vertex graph in which any two nonadjacent vertices have degree-sum at least n+k, then G has a spanning cycle containing any specified family of disjoint paths with a total of k edges. We consider the analogous problem for a bipartite graph G with n vertices and parts o
On independent cycles and edges in graphs
β Scribed by Thomas Andreae
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 339 KB
- Volume
- 149
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
For integers k, s with 0 ~ ~~2 and n >~ 3~ -s. Justesen (1989) determined ex(n, k, 0) for all n >~ 3k and EX(n,k,O) for all n > (13k -4)/4, thereby settling a conjecture of Erdrs and P6sa; further EX (n,k,k) was determined by Erdrs and Gallai (n>~2k). In the present paper, by modifying the argument presented by Justesen, we determine EX(n,k,s) for all n,k,s (0~~2, n>~3k -s).~~
π SIMILAR VOLUMES
A graph G of order n is a ck-graph if for every pair of d~tinct, nonadlacenl veJtlces x and y' d(x)+d(y)>~n+k where d(v) denotes the degree of a vertex v In this paper, we prove the
Let the reals be extended to include oo with o~ > r
An edge of a 3-connected graph is contractible if its contraction results in a graph which is still 3-connected. All 3-connected graphs with seven or more vertices are known to have at least three contractible edges on any longest cycle. Recently, it has been conjectured that any non-Hamiltonian 3-c
## Abstract Given a digraph __D__ on vertices __v__~1~, __v__~2~, β, __v__~__n__~, we can associate a bipartite graph __B(D)__ on vertices __s__~1~, __s__~2~, β, __s__~__n__~, __t__~1~, __t__~2~, β, __t__~__n__~, where __s__~__i__~__t__~__j__~ is an edge of __B(D)__ if (__v__~__i__~, __v__~__j__~)