## Abstract

A graph G homogeneously embeds in a graph H if for every vertex x of G and every vertex yof 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 f_{k}(G) (respectively, g_{k}(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 f_{2}(G) and g_{2}(G) for special classes of G, in particular when G is a star or balanced complete bipartite graph. Then we investigate f_{k}(G) and g_{k}(G) when k ≤ 3 and G is a complete graph.

Original language | English |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Quaestiones Mathematicae |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2005 |

Externally published | Yes |

## Keywords

- Bicliques
- Cliques
- Homogeneously embeds
- K-edge-colouring
- Stars
- Uniformly embeds

## ASJC Scopus subject areas

- Mathematics (miscellaneous)