Let (G, w ) denote a simple graph G with a weight function w : โฌ(G) -{0,1,2}. A path cover of (G, w ) is a collection of paths in G such that every edge e is contained in exactly w(e) paths of the collection. For a vertex u , w ( v ) is the sum of the weights of the edges incident with U ; U is call
m_Path Cover Saturated Graphs
โ Scribed by Aneta Dudek; Gyula Y. Katona; A.Pawel Wojda
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 258 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract A __perfect path double cover__ (PPDC) of a graph __G__ on __n__ vertices is a family ๐ซ of __n__ paths of __G__ such that each edge of __G__ belongs to exactly two members of ๐ซ and each vertex of __G__ occurs exactly twice as an end of a path of ๐ซ. We propose and study the conjecture th
Let G = (V,E) be a block graph. First we show that an algorithm for finding the path partition number p(G) by J.H. Yan and G.J. Chang gives wrong answers to some block graphs. Then we present an efficient algorithm for finding a minimum path partition of G (not just the path partition number p(G)).
## Abstract We prove in this paper that every simple graph __G__ admits a perfect path double cover (PPDC), i.e., a set of paths of __G__ such that each edge of __G__ belongs to exactly two of the paths and each vertex of __G__ is an end of exactly two of the paths, where a path of length zero is c