AbstractWe consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the following conjecture by B. Bollobás and P. Erdős (1976): if G is an edge-coloured complete graph on n vertices in which the maximum monochromatic degree of every vertex is less than ⌞n2⌟, then G contains a PC Hamiltonian cycle. We prove that if an edge-coloured complete graph contains a PC 2-factor then it has a PC Hamiltonian path. R. Häggkvist (1996) announced that every edge-coloured complete graph satisfying Bollobás-Erdős condition contains a PC 2-factor. These two results imply that every edge-coloured complete graph satisfying Bollobás-Erdo&#...
A c-edge-colored multigraph has each edge colored with one of the c available colors and no two para...
Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colo...
A graph G is Hamiltonian-connected if every two vertices of G are connected by a Hamilton path. A bi...
It is shown that, for >0 and n>n0(), any complete graph K on n vertices whose edges are colored so t...
A c-edge-colored multigraph has each edge colored with one of the c available colors and no two para...
A path (cycle) is properly-colored if consecutive edges are of distinct colors. In 1997, Bang-Jensen...
Let Kcn denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(...
Given a c-edge-coloured multigraph, where c is a positive integer, a proper Hamiltonian path is a pa...
AbstractIn an edge-colored graph, let dc(v) be the number of colors on the edges incident to v and l...
Let G be an edge-colored graph. The minimum color degree of G is the minimum number of different col...
An edge-colored graph is a graph with each edge assigned a color. A properly colored cycle ( or PC c...
AbstractLet Kn be the complete graph with vertex set {v1, v2, …, vn} and let g=(g1, …, gn) be a sequ...
A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colo...
AbstractA subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors...
AbstractLet G be a complete graph Kp (or a complete bipartite graph Km,m) with its lines colored so ...
A c-edge-colored multigraph has each edge colored with one of the c available colors and no two para...
Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colo...
A graph G is Hamiltonian-connected if every two vertices of G are connected by a Hamilton path. A bi...
It is shown that, for >0 and n>n0(), any complete graph K on n vertices whose edges are colored so t...
A c-edge-colored multigraph has each edge colored with one of the c available colors and no two para...
A path (cycle) is properly-colored if consecutive edges are of distinct colors. In 1997, Bang-Jensen...
Let Kcn denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(...
Given a c-edge-coloured multigraph, where c is a positive integer, a proper Hamiltonian path is a pa...
AbstractIn an edge-colored graph, let dc(v) be the number of colors on the edges incident to v and l...
Let G be an edge-colored graph. The minimum color degree of G is the minimum number of different col...
An edge-colored graph is a graph with each edge assigned a color. A properly colored cycle ( or PC c...
AbstractLet Kn be the complete graph with vertex set {v1, v2, …, vn} and let g=(g1, …, gn) be a sequ...
A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colo...
AbstractA subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors...
AbstractLet G be a complete graph Kp (or a complete bipartite graph Km,m) with its lines colored so ...
A c-edge-colored multigraph has each edge colored with one of the c available colors and no two para...
Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of Kn with n colo...
A graph G is Hamiltonian-connected if every two vertices of G are connected by a Hamilton path. A bi...