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June 2002 Degree-Sum Conditions for Graphs to Have 2-Factors with Cycles Through Specified Vertices
Toshinori Sakai
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SUT J. Math. 38(2): 211-222 (June 2002). DOI: 10.55937/sut/1057898618

Abstract

Let k2 and n1 be integers, let G be a graph of order n with minimum degree at least k + 1. Let υ1,υ2,,υk be k distinct vertices of G, and suppose that there exist k vertex disjoint cycles C1,,Ck in G such that υiV(Ci) for each 1ik. Suppose further that the minimum value of the sum of the degrees of two nonadjacent distinct vertices is greater than or equal to n+k43. Under these assumptions, we show that there is a 2-factor of G with k cycles D1,D2,,Dk such that υiV(Di) for each 1ik.

Citation

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Toshinori Sakai. "Degree-Sum Conditions for Graphs to Have 2-Factors with Cycles Through Specified Vertices." SUT J. Math. 38 (2) 211 - 222, June 2002. https://doi.org/10.55937/sut/1057898618

Information

Received: 11 November 2002; Published: June 2002
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1057898618

Subjects:
Primary: 05C38 , 05C70

Keywords: Degree-sum condition , Two-factor

Rights: Copyright © 2002 Tokyo University of Science

Vol.38 • No. 2 • June 2002
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