Star Colourings of Subdivisions
نویسنده
چکیده
Let G be a graph with chromatic number (G) and maximum degree (G). A star colouring of G is a function that assigns a colour to each vertex such that adjacent vertices receive distinct colours, and there is no bichromatic 4-vertex path. The star chromatic number st(G) is the minimum number of colours in a star colouring of G. Star colourings of subdivisions of graphs are investigated. Let G0 be the graph obtained from G by subdividing each edge once. Bounds on st(G0) in terms of (G) and (G) are proved. In particular, st(G0) maxf (G); 3g and st(G0) p (G) + 3. Furthermore, if st(G0) k then (G) k 22k. Hence st(G0) is tied to (G). On the other hand, a graph H obtained from G by subdividing each edge at least twice has st(H) 4.
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