Hamiltonicity of k-traceable graphs

Abstract

Let G be a graph. A Hamilton path in G is a path containing every vertex of G. The graph G is traceable if it contains a Hamilton path, while G is k-traceable if every induced subgraph of G of order k is traceable. In this paper, we study hamiltonicity of k-traceable graphs. For k ≥ 2 an integer, we define H(k) to be the largest integer such that there exists a k-traceable graph of order H(k) that is nonhamiltonian. For k ≤ 10, we determine the exact value of H(k). For k ≥ 11, we show that k + 2 ≤ H(k) ≤ 1/2 (3k - 5).