A Combinatorial Algorithm to Optimally Colour the Edges of the Graphs That Are Join of Regular Graphs

Authors:
Caterina Simone;Anna Galluccio
Affiliations:
Istituto di Analisi dei Sistemi ed Informatica, CNR, Rome, Italy 00185;Istituto di Analisi dei Sistemi ed Informatica, CNR, Rome, Italy 00185
Venue:
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Year:
2008

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Abstract

We prove that the edges of every even graph G= G1+ G2that is the join of two regular graphs Gi= (Vi,Ei) can be coloured with Δ(G) colours, whenever Δ(G) = Δ(G2) + |V(G1)|. The proof of this result yields a combinatorial algorithm to optimally colour the edges of this type of graphs.