## Abstract The path number of a graph __G__, denoted __p(G)__, is the minimum number of edgeβdisjoint paths covering the edges of __G.__ LovΓ‘sz has proved that if __G__ has __u__ odd vertices and __g__ even vertices, then __p(G)__ β€ 1/2 __u__ + __g__ β 1 β€ __n__ β 1, where __n__ is the total numbe
An Upper Bound for the Clar Number of Fullerene Graphs
β Scribed by Heping Zhang; Dong Ye
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 337 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0259-9791
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In this paper we consider those graphs that have maximum degree at least 1/__k__ times their order, where __k__ is a (small) positive integer. A result of Hajnal and SzemerΓ©di concerning equitable vertexβcolorings and an adaptation of the standard proof of Vizing's Theorem are used to s
An upper bound for the harmonious chromatic number of a graph G is given. Three corollaries of the theorem are theorems or improvements of the theorems of Miller and Pritikin. The assignment of colors to the vertices of a graph such that each vertex has exactly one color has been studied for well o
The kdomination number of a graph G, y k ( G ) , is the least cardinality of a set U of verticies such that any other vertex is adjacent to at least k vertices of U. We prove that if each vertex has degree at least k. then YAG) 5 kp/(k + 1).