## Abstract Let __G__ be a graph of order 4__k__ and let Ξ΄(__G__) denote the minimum degree of __G__. Let __F__ be a given connected graph. Suppose that |__V__(__G__)| is a multiple of |__V__(__F__)|. A spanning subgraph of __G__ is called an __F__βfactor if its components are all isomorphic to __F
The virtual k-factorability of graphs
β Scribed by Seiya Negami
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 340 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
It is shown that if a connected graph G admits a finite covering that has a k-factor, then there is a 1 -or 2-fold covering of G that has a k-factor and that such a covering can be given as a canonical bipartite graph associated with G.
will conflict with the first one in Czn-, but there is no trouble in C,,,_? since the two corresponding choices arise at different places. This suggests that a covering would simplify some obstruction to 1-factors.
π SIMILAR VOLUMES
## Abstract We show that every connected __K__~1,3~βfree graph with minimum degree at least __2k__ contains a __k__βfactor and construct connected __K__~1,3~βfree graphs with minimum degree __k__ + __0__(β__k__) that have no __k__βfactor.
## Abstract A graph is said to be __K__~1,__n__~βfree, if it contains no __K__~1,__n__~ as an induced subgraph. We prove that for __n__ β©Ύ 3 and __r__ β©Ύ __n__ β1, if __G__ is a __K__~1,__n__~βfree graph with minimum degree at least (__n__^2^/4(__n__ β1))__r__ + (3__n__ β6)/2 + (__n__ β1)/4__r__, the
## Abstract A 1βfactorization is constructed for the line graph of the complete graph __K~n~__ when __n__ is congruent to 0 or 1 modulo 4.