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- W1980334956 abstract "A new upper bound is proved for the chromatic index $q^* ( G )$ of multigraphs $G = ( V,E )$. Let $d ( G )$ be the maximum degree of G, and let [ p ( G ) = text{MAX} { lceil 2 | E(X) |/ ( | X | - 1) rceil :X subset V, | X | ne 1,text{and odd} } ] where $E( X )$ is the set of edges in the subgraph of G induced by X. The upper bound is expressed in terms of the two trivial lower bounds $d ( G )$ and $p ( G )$ as follows: [ q^* ( G )leqq text{MAX} { p ( G ), lfloor 1.1 d ( G ) + 0.8 rfloor }. ] The proof yields an algorithm which edge-colors any given multigraph G with at most $lfloor 1.1q^* ( G ) + 0.8 rfloor $ colors. The running time is $O ( | E | ( d ( G ) + | V | ) )$ and the storage space is $O ( | E | )$." @default.
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- W1980334956 date "1990-08-01" @default.
- W1980334956 modified "2023-09-26" @default.
- W1980334956 title "On the $1.1$ Edge-Coloring of Multigraphs" @default.
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- W1980334956 doi "https://doi.org/10.1137/0403035" @default.
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