Add to ORKGAbstract: Let G be a graph of order n satisfying d(u) + d(v) n for every edge uv of G. We show that the circumference|the length of a longest cycle|of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length between 3 and the circumference, unless G is complete bipartite. If G is 1-tough then it is pancyclic or G = Kr;r with r = n=2. c © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 253{256, 199
We discuss recent algorithmic extensions of two classic results of extremal combinatorics about long...
For a graph G, p(G) denotes the order of a longest path in G and c(G) the order of a longest cycle. ...
AbstractFor a graph G, p(G) and c(G) denote the orders of a longest path and a longest cycle of G, r...
Let G be a graph of order n satisfying d(u) + d(v) n for every edge uv of G. We show that the circum...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractIn this paper, we consider the length of the longest cycle through specified vertices. We sh...
In 1959, Erdős and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a ...
Our main result is the following theorem. Let k ≥ 2 be an integer, G be a graph of sufficiently larg...
Karger, Motwani and Ramkumar have shown that there is no constant approximation algorithm to find a ...
AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one o...
AbstractLet C be a longest cycle in a connected graph G and L(G) the length of the longest path in G...
AbstractA cycle C in an undirected and simple graph G is dominating if G - C is edgeless. A graph G ...
Karger, Motwani, and Ramkumar [Algorithmica, 18 (1997), pp. 82–98] have shown that there is no const...
We present and prove several results concerning the length of longest cycles in 2-connected or I-tou...
We discuss recent algorithmic extensions of two classic results of extremal combinatorics about long...
For a graph G, p(G) denotes the order of a longest path in G and c(G) the order of a longest cycle. ...
AbstractFor a graph G, p(G) and c(G) denote the orders of a longest path and a longest cycle of G, r...
Let G be a graph of order n satisfying d(u) + d(v) n for every edge uv of G. We show that the circum...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractIn this paper, we consider the length of the longest cycle through specified vertices. We sh...
In 1959, Erdős and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a ...
Our main result is the following theorem. Let k ≥ 2 be an integer, G be a graph of sufficiently larg...
Karger, Motwani and Ramkumar have shown that there is no constant approximation algorithm to find a ...
AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one o...
AbstractLet C be a longest cycle in a connected graph G and L(G) the length of the longest path in G...
AbstractA cycle C in an undirected and simple graph G is dominating if G - C is edgeless. A graph G ...
Karger, Motwani, and Ramkumar [Algorithmica, 18 (1997), pp. 82–98] have shown that there is no const...
We present and prove several results concerning the length of longest cycles in 2-connected or I-tou...
We discuss recent algorithmic extensions of two classic results of extremal combinatorics about long...
For a graph G, p(G) denotes the order of a longest path in G and c(G) the order of a longest cycle. ...
AbstractFor a graph G, p(G) and c(G) denote the orders of a longest path and a longest cycle of G, r...