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Keywords:

  • enclosing;
  • 5-cycles;
  • Skolem sequences

Abstract

A k-cycle system of a multigraph G is an ordered pair (V, C) where V is the vertex set of G and C is a set of k-cycles, the edges of which partition the edges of G. A k-cycle system of inline image is known as a λ-fold k-cycle system of order V. A k-cycle system of inline image (V, C) is said to be enclosed in a k-cycle system of inline image inline image if inline image and inline image. We settle the difficult enclosing problem for λ-fold 5-cycle systems with u = 1.