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- W3136351945 abstract "We wish to bring attention to a natural but slightly hidden problem, posed by Erdős and Nesetřil in the late 1980s, an edge version of the degree–diameter problem. Our main result is that, for any graph of maximum degree (varDelta ) with more than (1.5 varDelta ^t) edges, its line graph must have diameter larger than t. In the case where the graph contains no cycle of length (2t+1), we can improve the bound on the number of edges to one that is exact for (tin {1,2,3,4,6}). In the case (varDelta =3) and (t=3), we obtain an exact bound. Our results also have implications for the related problem of bounding the distance-t chromatic index, (t>2); in particular, for this we obtain an upper bound of (1.941varDelta ^t) for graphs of large enough maximum degree (varDelta ), markedly improving upon earlier bounds for this parameter." @default.
- W3136351945 created "2021-03-29" @default.
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- W3136351945 date "2021-01-01" @default.
- W3136351945 modified "2023-09-25" @default.
- W3136351945 title "Maximising Line Subgraphs of Diameter at Most t" @default.
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- W3136351945 doi "https://doi.org/10.1007/978-3-030-83823-2_52" @default.
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