Geodesic
Rainbow matchings of size \(m\) in graphs with total color degree at least \(2mn\)
Jürgen Kritschgau1
1Iowa State University
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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The existence of a rainbow matching given a minimum color degree, proper coloring, or triangle-free host graph has been studied extensively. This paper generalizes these problems to edge colored graphs with given total color degree. In particular, we find that if a graph $G$ has total color degree $2mn$ and satisfies some other properties, then $G$ contains a matching of size $m$. These other properties include $G$ being triangle-free, $C_4$-free, properly colored, or large enough.
DOI : 10.37236/8239
Classification : 05C15, 05C70
Mots-clés : edge colored graphs with given total color degree

Jürgen Kritschgau  1

1 Iowa State University 
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     author = {J\"urgen Kritschgau},
     title = {Rainbow matchings of size \(m\) in graphs with total color degree at least \(2mn\)},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {3},
     doi = {10.37236/8239},
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Jürgen Kritschgau. Rainbow matchings of size \(m\) in graphs with total color degree at least \(2mn\). The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8239

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