An edge-colored graph G is k-proper connected if every pair of vertices is connected by k
internally pairwise vertex-disjoint proper colored paths. The k-proper connection number of …

Generalizations of Dirac’s theorem in Hamiltonian graph theory—A survey - ScienceDirect
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For a 2-connected graph G, the relative length of G, denoted by diff (G), is the difference
between the orders of a longest path and a longest cycle in G. This parameter is used as a …

Let G be a triangle-free graph of order n and minimum degree δ> n∕ 3. We will determine
all lengths of cycles occurring in G. In particular, the length of a longest cycle or path in G is …

For a graph G, let p (G) denote the order of a longest path in G and c (G) the order of a
longest cycle in G, respectively. We show that if G is a 3‐connected graph of order n such …

Two sufficient conditions for dominating cycles Page 1 Two Sufficient Conditions for Dominating
Cycles Mei Lu,1 Huiqing Liu,2 and Feng Tian2 1DEPARTMENT OF MATHEMATICAL SCIENCES …

For a graph G, p (G) and c (G) denote the order of a longest path and a longest cycle of G,
respectively. In this paper, we prove that if G is a 3‐connected graph of order n such that the …

Let G be a graph. We denote p (G) and c (G) the order of a longest path and the order of a
longest cycle of G, respectively. Let κ (G) be the connectivity of G, and let σ 3 (G) be the …

Win, in 1975, and Jackson and Wormald, in 1990, found the best sufficient conditions on the
degree sum of a graph to guarantee the properties of “having a k-tree” and “having a k …

For a graph G, p (G) and c (G) denote the orders of a longest path and a longest cycle of G,
respectively. For a graph G, we denote by dG (x) and κ (G) the degree of a vertex x in G and …