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Abstract
Let G be an edgecoloured graph. A rainbow subgraph in G is a subgraph such that its edges have distinct colours. The minimum colour degree δ^{c}(G) of G is the smallest number of distinct colours on the edges incident with a vertex of G. We show that every edgecoloured graph G on n≥7k/2+2 vertices with δ^{c}(G)≥k contains a rainbow matching of size at least k, which improves the previous result for k≥10.
Let Δ_{mon(G) be the maximum number of edges of the same colour incident with a vertex of G. We also prove that if t≥11 and Δmon(G)≤t, then G can be edgedecomposed into at most ⌊tn/2⌋ rainbow matchings. This result is sharp and improves a result of LeSaulnier and West.}
Let Δ_{mon(G) be the maximum number of edges of the same colour incident with a vertex of G. We also prove that if t≥11 and Δmon(G)≤t, then G can be edgedecomposed into at most ⌊tn/2⌋ rainbow matchings. This result is sharp and improves a result of LeSaulnier and West.}
Original language  English 

Pages (fromto)  21192124 
Number of pages  6 
Journal  Discrete Mathematics 
Volume  338 
Early online date  9 Jun 2015 
DOIs  
Publication status  Published  6 Nov 2015 
Keywords
 Edge coloring
 Rainbow
 Matching
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Dive into the research topics of 'Existences of rainbow matchings and rainbow matching covers'. Together they form a unique fingerprint.Projects
 1 Finished

FP7 ERC  QRGraph: Quasirandomness in Graphs and Hypergraphs
European Commission, European Commission  Management Costs
1/12/10 → 30/11/15
Project: Research