# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

## ON TRACEABILITY AND 2-FACTORS IN CLAW-FREE GRAPHS

 Dalibor Froncek Department of Mathematics and StatisticsUniversity of Minnesota DuluthDuluth, MN 55810, U.S.A.andDepartment of Applied MathematicsTechnical University of OstravaOstrava, Czech Republice-mail: dfroncek@d.umn.edu Zdenek Ryjácek Department of MathematicsUniversity of West BohemiaandInstitute of Theoretical Computer ScienceCharles UniversityUniverzitní 8, 306 14 Plzen, Czech Republice-mail: ryjacek@kma.zcu.cz Zdzisław Skupień Faculty of Applied MathematicsUniversity of Mining and Metallurgy AGHal. Mickiewicza 30, 30-059 Kraków, Polande-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 = 18 C i or is traceable.

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

2000 Mathematics Subject Classification: 05C45, 05C70.

## References

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