Spanning Cyclic Subdivisions of Vertex-Disjoint Cycles and Chorded Cycles in Graphs

摘要

Let G be a graph on n ≥ 3 vertices and H be a subgraph of G such that each component of H is a cycle with at most one chord. In this paper we prove that if the minimum degree of G is at least n/2, then G contains a spanning subdivision of H such that only non-chord edges of H are subdivided. This gives a new generalization of the classical result of Dirac on the existence of Hamilton cycles in graphs.