Geodesic
Partitions and edge colourings of multigraphs
The electronic journal of combinatorics, Tome 15 (2008)

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Erdős and Lovász conjectured in 1968 that for every graph $G$ with $\chi(G)>\omega(G)$ and any two integers $s,t\geq 2$ with $s+t=\chi(G)+1$, there is a partition $(S,T)$ of the vertex set $V(G)$ such that $\chi(G[S])\geq s$ and $\chi(G[T])\geq t$. Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for line graphs of multigraphs.
DOI : 10.37236/900
Classification : 05C15, 05C70 
Alexandr V. Kostochka; Michael Stiebitz. Partitions and edge colourings of multigraphs. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/900
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     title = {Partitions and edge colourings of multigraphs},
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     year = {2008},
     volume = {15},
     doi = {10.37236/900},
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