Independent triangles covering given vertices of a graph

• Authors: Hao Li;Jianping Li
• Venue: Theoretical Computer Science
• Year: 2001

Let G be a simple graph of order n, k a positive integer with n≥3k and X a set of any k vertices of G. We show that if the minimum degree G)≥(n + k)=2, then G contains k independent triangles covering all vertices of X ; and if the minimum degree (G)≥(n+2k)=2, then G contains k independent triangles such that each triangle contains exactly one vertex of X . The bounds on the minimum degree of G in above results are sharp. Some conjectures about independent triangles covering some given vertices are proposed.