## 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 on the path number of a digraph
β Scribed by Richard C O'Brien
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 431 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The upper bound for the harmonious chromatic number of a graph that has been given by SinβMin Lee and John Mitchem is improved.
## Abstract We draw the __n__βdimensional hypercube in the plane with ${5\over 32}4^{n}-\lfloor{{{{n}^{2}+1}\over 2}}\rfloor {2}^{n-2}$ crossings, which improves the previous best estimation and coincides with the long conjectured upper bound of ErdΓΆs and Guy. Β© 2008 Wiley Periodicals, Inc. J Graph
## Abstract A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number Ο^__c__^. Let Ξ^\*^ be the maximum face degree of a graph. There exist