The mean chromatic number of a graph is defined. This is a measure of the expected performance of the greedy vertex-colouring algorithm when each ordering of the vertices is equally likely. In this note, we analyse the asymptotic behaviour of the mean chromatic number for the paths and even cycles,
On the number of increasing paths in labeled cycles and stars
✍ Scribed by Lei Chen; Changhong Lü; Yongsheng Ye
- Book ID
- 107500757
- Publisher
- SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
- Year
- 2007
- Tongue
- English
- Weight
- 119 KB
- Volume
- 22
- Category
- Article
- ISSN
- 1005-1031
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The tensor product of graphs G1 and G2 is defined to be G= (V,E) where V = V(Gl ) x V(G2) and edge ((x~,.YI),(x~,Yz)) EE whenever (xI,xz)EE(GI) and (yl,yz)~E(G2). We use GI(Tp)G2 to denote G. This paper establishes the bandwidth of the tensor product of a path with a path, a cycle with a path, and
It is proved that if a planar triangulation different from K3 and K4 contains a Hamiltonian cycle, then it contains at least four of them. Together with the result of Hakimi, Schmeichel, and Thomassen [21, this yields that, for n 2 12, the minimum number of Hamiltonian cycles in a Hamiltonian planar