Covering Graphs by Monochromatic Trees and Helly-Type Results for Hypergraphs
نویسندگان
چکیده
How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given r-edge-coloured graph G? These problems were introduced in the 1960s and intensively studied by various researchers over last 50 years. In this paper, we establish connection between problem following natural Helly-type question hypergraphs. Roughly speaking, asks for maximum number needed edges hypergraph H if it is known that any collection few has small cover. We obtain quite accurate bounds use them give some unexpected answers several questions about covering graphs raised Bal DeBiasio, Kohayakawa, Mota Schacht, Lang Lo, Cirão, Letzter Sahasrabudhe.
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2021
ISSN: ['0209-9683', '1439-6912']
DOI: https://doi.org/10.1007/s00493-020-4292-9