Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On parsimonious edge-colouring of graphs with maximum degree three   In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest
fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showed
that $\gamma \geq 13/15$ when $G$ is cubic . We show here that this result can
be extended to graphs with maximum degree 3 with the exception of a graph on 5
vertices. Moreover, there are exactly two graphs with maximum degree 3 (one
being obviously the Petersen graph) for which $\gamma = 13/15$. This extends a
result given by Steffen. These results are obtained by using structural
properties of the so called $\delta$-minimum edge colourings for graphs with
maximum degree 3. Keywords : Cubic graph; Edge-colouring

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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th