Polynomial bounds for chromatic number. I. Excluding a biclique and an induced tree
نویسندگان
چکیده
Let H H be a tree. It was proved by Rödl that graphs do not contain altimg="urn:x-wiley:03649024:media:jgt22880:jgt22880-math-0002" wiley:location="equation/jgt22880-math-0002.png">H as an induced subgraph, and the complete bipartite graph K t , altimg="urn:x-wiley:03649024:media:jgt22880:jgt22880-math-0003" wiley:location="equation/jgt22880-math-0003.png">Kt,t have bounded chromatic number. Kierstead Penrice strengthened this, showing such degeneracy. Here we give further strengthening, proving for every tree altimg="urn:x-wiley:03649024:media:jgt22880:jgt22880-math-0004" wiley:location="equation/jgt22880-math-0004.png">H degeneracy is at most polynomial in altimg="urn:x-wiley:03649024:media:jgt22880:jgt22880-math-0005" wiley:location="equation/jgt22880-math-0005.png">t . This answers question of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, Walczak.
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2022
ISSN: ['0364-9024', '1097-0118']
DOI: https://doi.org/10.1002/jgt.22880