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- W4299489609 abstract "We consider graphs $G$ with $Delta=3$ such that $chi'(G)=4$ and $chi'(G-e)=3$ for every edge $e$, so-called emph{critical} graphs. Jakobsen noted that the Petersen graph with a vertex deleted, $P^*$, is such a graph and has average degree only $frac83$. He showed that every critical graph has average degree at least $frac83$, and asked if $P^*$ is the only graph where equality holds. A result of Cariolaro and Cariolaro shows that this is true. We strengthen this average degree bound further. Our main result is that if $G$ is a subcubic critical graph other than $P^*$, then $G$ has average degree at least $frac{46}{17}approx2.706$. This bound is best possible, as shown by the Hajos join of two copies of $P^*$." @default.
- W4299489609 created "2022-10-02" @default.
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- W4299489609 date "2015-06-13" @default.
- W4299489609 modified "2023-10-16" @default.
- W4299489609 title "Subcubic edge chromatic critical graphs have many edges" @default.
- W4299489609 doi "https://doi.org/10.48550/arxiv.1506.04225" @default.
- W4299489609 hasPublicationYear "2015" @default.
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