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Discussiones Mathematicae Graph Theory 24(1) (2004) 55-71
DOI: https://doi.org/10.7151/dmgt.1213

ON TRACEABILITY AND 2-FACTORS IN CLAW-FREE GRAPHS

Dalibor Froncek

Department of Mathematics and Statistics
University of Minnesota Duluth
Duluth, MN 55810, U.S.A.
and
Department of Applied Mathematics
Technical University of Ostrava
Ostrava, Czech Republic
e-mail: dfroncek@d.umn.edu

Zdenek Ryjácek

Department of Mathematics
University of West Bohemia
and
Institute of Theoretical Computer Science
Charles University
Univerzitní 8, 306 14 Plzen, Czech Republic
e-mail: ryjacek@kma.zcu.cz

Zdzisław Skupień

Faculty of Applied Mathematics
University of Mining and Metallurgy AGH
al. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: skupien@uci.agh.edu.pl

Abstract

If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σ _k > n+k²− 4k+7 (where k is an arbitrary constant), then G has a 2-factor with at most k− 1 components. As a second main result, we present classes of graphs C ₁,… ,C ₈ such that every sufficiently large connected claw-free graph satisfying degree condition σ ₆ (k) > n+19 (or, as a corollary, δ (G) > [(n+19)/6]) either belongs to ∪ _{i = 1}⁸ C _i or is traceable.

Keywords: traceability, 2-factor, claw, degree condition, closure

2000 Mathematics Subject Classification: 05C45, 05C70.

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Received 29 May 2001
Revised 14 November 2002