## Abstract A path on __n__ vertices is denoted by __P__~__n__~. For any graph __H__, the number of isolated vertices of __H__ is denoted by __i(H)__. Let __G__ be a graph. A spanning subgraph __F__ of __G__ is called a {__P__~3~, __P__~4~, __P__~5~}βfactor of __G__ if every component of __F__ is o
Path factors in cubic graphs
β Scribed by Ken-ichi Kawarabayashi; Haruhide Matsuda; Yoshiaki Oda; Katsuhiro Ota
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 67 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
Pullman [3] conjectured that if k is an odd positive integer, then every orientation of a regular graph of degree k has a minimum decomposition which contains no vertex which is both the initial vertex of some path in the decomposition and the terminal vertex of some other path in the decomposition
## Abstract The path layer matrix (or path degree sequence) of a graph __G__ contains quantitative information about all paths in __G__. The entry (__i,j__) in this matrix is the number of simple paths in __G__ having initial vertex __v__ and length __j.__ It was known that there are cubic graphs o
## Abstract The path layer matrix (or path degree sequence) of a graph __G__ contains quantitative information about all possible paths in __G__. The entry (__i,j__) of this matrix is the number of paths in __G__ having initial vertex __i__ and length __j__. It is known that there are cubic graphs
## Abstract In this paper we show that every simple cubic graph on __n__ vertices has a set of at least ββ__n__/4ββ disjoint 2βedge paths and that this bound is sharp. Our proof provides a polynomial time algorithm for finding such a set in a simple cubic graph. Β© 2003 Wiley Periodicals, Inc. J Gra