A graph is called uniquely k-colorable if there is only one partition of its vertex set into k color classes. The first result of this note is that if a k-colorable graph G of order n is such that its minimal degree, δ(G), is greater than (3k−5)/(3k−2) n then it is uniquely k-colorable. This result can be strengthened considerably if one considers only graphs having an obvious property of k-colorable graphs. More precisely, the main result of the note states the following. If G is a graph of order n that has a k-coloring in which the subgraph induced by the union of any two color classes is connected then δ(G)>(1−(1/(k−1))) n implies that G is uniquely k-colorable. Both these results are best possible
Abstract: This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The mai...
AbstractA graph is (m,k)-colorable if its vertices can be colored with m colors in such a way that e...
The study of graph vertex colorability from an algebraic perspective has introduced novel techniques...
A graph is called uniquely k-colorable if there is only one partition of its vertex set into k color...
A graph is called uniquely k-colorable if there is only one partition of its vertex set into k color...
AbstractWe show the following. (1) For each integer n⩾12, there exists a uniquely 3-colorable graph ...
AbstractA labeled graph G with chromatic number n is called uniquely n-colorable or simply uniquely ...
AbstractFor integers k⩾1 and m⩾2 a (k,m)-colouring of a graph G is a colouring of the vertices of G ...
AbstractFor n ≥ 3, if there exists a uniquely n colorable graph which contains no subgraph isomorphi...
A graph $G$ is {\it uniquely k-edge-colorable} if the chromatic index of $G$ is $k$ and every two $k...
AbstractFor a graph G, the path number τ(G) is defined as the order of a longest path in G. An (m, k...
Given a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a proper ver...
The author can archive pre-print, post-print of the article. appropriate journal homepage link is a...
AbstractGiven graphs F and G and a nonnegative integer k, a function π : V(F) → 1, …, k is a −G k-co...
AbstractGiven a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a pr...
Abstract: This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The mai...
AbstractA graph is (m,k)-colorable if its vertices can be colored with m colors in such a way that e...
The study of graph vertex colorability from an algebraic perspective has introduced novel techniques...
A graph is called uniquely k-colorable if there is only one partition of its vertex set into k color...
A graph is called uniquely k-colorable if there is only one partition of its vertex set into k color...
AbstractWe show the following. (1) For each integer n⩾12, there exists a uniquely 3-colorable graph ...
AbstractA labeled graph G with chromatic number n is called uniquely n-colorable or simply uniquely ...
AbstractFor integers k⩾1 and m⩾2 a (k,m)-colouring of a graph G is a colouring of the vertices of G ...
AbstractFor n ≥ 3, if there exists a uniquely n colorable graph which contains no subgraph isomorphi...
A graph $G$ is {\it uniquely k-edge-colorable} if the chromatic index of $G$ is $k$ and every two $k...
AbstractFor a graph G, the path number τ(G) is defined as the order of a longest path in G. An (m, k...
Given a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a proper ver...
The author can archive pre-print, post-print of the article. appropriate journal homepage link is a...
AbstractGiven graphs F and G and a nonnegative integer k, a function π : V(F) → 1, …, k is a −G k-co...
AbstractGiven a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a pr...
Abstract: This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The mai...
AbstractA graph is (m,k)-colorable if its vertices can be colored with m colors in such a way that e...
The study of graph vertex colorability from an algebraic perspective has introduced novel techniques...