This article is intended as a survey, updating earlier surveys in the area. For completeness
of the presentation of both particular questions and the general area, it also contains some …

Given a fixed positive integer k≥ 2 and a fixed pair of vertices x and y in a graph of
sufficiently large order n= n (k), minimum degree conditions that imply the existence of a …

Given a fixed positive integer k≥ 2, let G be a simple graph of order n≥ 6 k. It is proved that
if the minimum degree of G is at least n/2+ 1, then for every pair of vertices x and y, there …

Given k≥ 2 fixed positive integers p 1, p 2,…, pk− 1≥ 2, and k vertices {x 1, x 2,…, xk}, let G
be a simple graph of sufficiently large order n. It is proved that if δ (G)≥(n+ 2 k− 2)/2, then …

Abstract In 2000, Enomoto and Ota [J Graph Theory 34 (2000), 163–169] stated the
following conjecture. Let G be a graph of order n, and let n1, n2,…, nk be positive integers …

Given a multigraph H, a graph G is H-linked if every injective map f: V (H)−→ V (G) can be
extended into an H-subdivision in G. Given a multigraph H and an integer sequence D={dij …

In this paper, we consider the path (and cycle) partition problem for graphs with additional
length restrictions. More specifically, we prove sufficient degree sum conditions for the …

Let G be a graph of order n with minimum degree δ (G)\geqslant n 2+ 1 δ (G)⩾ n 2+ 1.
Faudree and Li (2012) conjectured that for any pair of vertices x and y in G and any integer …

Placing Specified Vertices at Precise Locations on a Hamiltonian Cycle | SpringerLink Skip to
main content Advertisement SpringerLink Log in Menu Find a journal Publish with us Search …

A cycle passing through all the vertices exactly once in a graph is a Hamiltonian cycle (HC).
In the field of network system, HC plays a vital role as it covers all the vertices in the system …