Add to ORKGWe prove that for all integers κ,s≥0 there exists c with the following property. Let G be a graph with clique number at most κ and chromatic number more than c. Then for every vertex-colouring (not necessarily optimal) of G, some induced subgraph of G is an s-vertex path, and all its vertices have different colours. This extends a recent result of Gyárfás and Sárközy (2016) who proved the same for graphs G with κ=2 and girth at least five
Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its interna...
A well-studied coloring problem is to assign colors to the edges of a graph G so that, for every pai...
AbstractFor a given graph H and n⩾1, let f(n,H) denote the maximum number m for which it is possible...
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle...
A colorful path in a graph G is a path with χ(G) vertices whose colors are differ-ent. A v-colorful ...
AbstractA k-rainbow path in a graph with colored edges is a path of length k where each edge has a d...
The most famous problem in Graph Theory is arguably one involving the coloring of graphs so that map...
In a proper vertex coloring of a graph a subgraph is colorful if its vertices are colored with dif...
A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. The ...
We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there...
In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the sa...
AbstractA colored graph is a graph whose vertices have been properly, though not necessarily optimal...
The concept of [r, s, t]-colourings was recently introduced by Hackmann, Kemnitz and Marangio [3] as...
A well-studied coloring problem is to assign colors to the edges of a graph G so that, for every pai...
Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its interna...
Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its interna...
A well-studied coloring problem is to assign colors to the edges of a graph G so that, for every pai...
AbstractFor a given graph H and n⩾1, let f(n,H) denote the maximum number m for which it is possible...
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle...
A colorful path in a graph G is a path with χ(G) vertices whose colors are differ-ent. A v-colorful ...
AbstractA k-rainbow path in a graph with colored edges is a path of length k where each edge has a d...
The most famous problem in Graph Theory is arguably one involving the coloring of graphs so that map...
In a proper vertex coloring of a graph a subgraph is colorful if its vertices are colored with dif...
A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. The ...
We prove that, for every graph $F$ with at least one edge, there is a constant $c_F$ such that there...
In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the sa...
AbstractA colored graph is a graph whose vertices have been properly, though not necessarily optimal...
The concept of [r, s, t]-colourings was recently introduced by Hackmann, Kemnitz and Marangio [3] as...
A well-studied coloring problem is to assign colors to the edges of a graph G so that, for every pai...
Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its interna...
Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its interna...
A well-studied coloring problem is to assign colors to the edges of a graph G so that, for every pai...
AbstractFor a given graph H and n⩾1, let f(n,H) denote the maximum number m for which it is possible...