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Spanning trees in graphs of high minimum degree with a universal vertex I: An asymptotic result

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Autor(es):
Reed, Bruce ; Stein, Maya
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: JOURNAL OF GRAPH THEORY; v. 102, n. 4, p. 47-pg., 2022-10-07.
Resumo

In this paper and a companion paper, we prove that, if m $m$ is sufficiently large, every graph on m + 1 $m+1$ vertices that has a universal vertex and minimum degree at least L 2 m 3 <SIC> RIGHT FLOOR $\lfloor \phantom{\rule[-0.5em]{}{0ex}}\frac{2m}{3}\rfloor $ contains each tree T $T$ with m $m$ edges as a subgraph. Our result confirms, for large m $m$, an important special case of a recent conjecture by Havet, Reed, Stein and Wood. The present paper already contains an approximate version of the result. (AU)

Processo FAPESP: 19/13364-7 - Problemas extremais e estruturais em teoria dos grafos
Beneficiário:Cristina Gomes Fernandes
Modalidade de apoio: Auxílio à Pesquisa - Regular