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On a cycle partition problem
Authors:Morten Hegner Nielsen
Institution:Department of Mathematics and Statistics, University of Winnipeg, Manitoba, Canada
Abstract:Let G be any graph and let c(G) denote the circumference of G. We conjecture that for every pair c1,c2 of positive integers satisfying c1+c2=c(G), the vertex set of G admits a partition into two sets V1 and V2, such that Vi induces a graph of circumference at most ci, i=1,2. We establish various results in support of the conjecture; e.g. it is observed that planar graphs, claw-free graphs, certain important classes of perfect graphs, and graphs without too many intersecting long cycles, satisfy the conjecture.This work is inspired by a well-known, long-standing, analogous conjecture involving paths.
Keywords:Circumference  Partition  Longest cycle  Path partition conjecture
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