For a graph G, the path number r(G) is defined as the order of a longest path in G. An (m, k)~-colouring of a graph H is a partition of the vertex set of H into m subsets such that each subset induces a subgraph of H for which r is at most k. The k -z-chromatic number z~(H) is the least m for which
On the order of uniquely (k,m)-colourable graphs
β Scribed by Izak Broere; Marietjie Frick
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 578 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0012-365X
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## Abstract A graph is chromatically unique if it is uniquely determined by its chromatic polynomial. Let __G__ be a chromatically unique graph and let __K__~__m__~ denote the complete graph on __m__ vertices. This paper is mainly concerned with the chromaticity of __K__~__m__~ + __G__ where + deno
Almtngt. Gi~ a ter~ph, p~tn every two vt~rticet which me 5t a dhtance tugateΒ’ than a fixed intelget k t>l) by a new path of lenltth k. Thus a laaph tranlfor:nati~n ts defined. The least number of itaslttior~ of tht, tr;m~l'ofmalion Such that the last it~rJfion does not change the graph. et called th