Induced trees in triangle-free graphs

We prove that every connected triangle-free graph on n vertices contains an induced tree on e x p ( c log n ) vertices, where c is a positive constant. The best known upper bound is ( 2 + o ( 1 ) ) n . This partially answers questions of Erdős, Saks, and Sós and of Pultr.

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 29; pp. 307 - 313
Main Authors Matoušek, Jiří, Šámal, Robert
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.08.2007
Subjects
induced subgraphs
trees
trees
induced subgraphs
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Summary:We prove that every connected triangle-free graph on n vertices contains an induced tree on e x p ( c log n ) vertices, where c is a positive constant. The best known upper bound is ( 2 + o ( 1 ) ) n . This partially answers questions of Erdős, Saks, and Sós and of Pultr.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2007.07.053