Partitions of a graph into paths with prescribed endvertices and lengths

  • Authors:

  • Hikoe Enomoto;Katsuhiro Ota

  • Affiliations:

  • Department of Mathematics, Keio University, Yokohama, 223-8522 Japan;Department of Mathematics, Keio University, Yokohama, 223-8522 Japan

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2000

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Abstract

For a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. We conjecture that if |V(G)| = n = Σki = 1 ai and σ2(G) ≥ n + k - 1, then for any k vertices v1, v2,…, vk in G, there exist vertex-disjoint paths P1, P2,…, Pk such that |V(Pi)| = ai and vi is an endvertex of Pi for 1 ≤ i ≤ k. In this paper, we verify the conjecture for the cases where almost all ai ≤ 5, and the cases where k ≤ 3. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 163–169, 2000