Vertex Coverings by Coloured Induced Graphs - Frames and Umbrellas

A graph G homogeneously embeds in a graph H if for every vertex x of G and every vertex y of H there is an induced copy of G in H with x at y. The graph G uniformly embeds in H if for every vertex y of H there is an induced copy of G in H containing y. For positive integer k, let fk(G) (respectively, gk(G)) be the minimum order of a graph H whose edges can be k-coloured such that for each colour, G homogeneously embeds (respectively, uniformly embeds) in the graph given by V (H) and the edges of that colour. We investigate the values f2(G) and g2(G) for special classes of G, in particular when G is a star or balanced complete bipartite graph. Then we investigate fk(G) and gk(G) when k 3 and G is a complete graph.

• Type: Journal
• Year: 2002
• Where: ENDM
• Authors: Wayne Goddard, Michael A. Henning
• Keywords: ENDM 2002, Minimum Order, Positive Integer, Special