We give a new upper bound on the total chromatic number of a graph. This bound improves the results known for some classes of graphs. The bound is stated as follows: ZT ~< Z~ + L l3 ~ J + 2, where Z is the chromatic number, Z~ is the edge chromatic number (chromatic index) and ZT is the total chroma
A tight upper bound for group testing in graphs
β Scribed by Peter Damaschke
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 481 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## 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
Given a finite graph G=( V, E), what is the minimum number c(G) of incidence tests which are needed in the worst case to identify an unknown edge e\*EE? The number c(G) was first studied by Aigner and Triesch (1988), where it was shown that for almost all graphs in the random graph model where d(n)