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Lower Bounds For Induced Forests in Cubic Graphs

Published online by Cambridge University Press:  20 November 2018

J. A. Bondy ,
Glenn Hopkins  and
William Staton
J. A. Bondy
Affiliation:
Faculty of Mathematics University of Waterloo Waterloo, Ontario, N2L 3G1
Glenn Hopkins
Affiliation:
Faculty of Mathematics University of Waterloo Waterloo, Ontario, N2L 3G1
William Staton
Affiliation:
Department of Mathematics University of Mississippi University, Mississippi, 38677
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Abstract

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If G is a connected cubic graph with ρ vertices, ρ > 4, then G has a vertex-induced forest containing at least (5ρ - 2)/8 vertices. In case G is triangle-free, the lower bound is improved to (2ρ — l)/3. Examples are given to show that no such lower bound is possible for vertex-induced trees.

Keywords

05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 193 - 199
Copyright
Copyright © Canadian Mathematical Society 1987

References

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4. Staton, W., Induced forests in cubic graphs, Discrete Mathematics 49 (1984) 175-178.Google Scholar