Let G be a simple graph and f : V (G) → {1, 3, 5, ...} an odd integer valued function defined on V (G). A spanning subgraph F of G is called a (1, f)odd factor if dF (v) ∈ {1...
A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
A weighted graph is one in which every edge e is assigned a nonnegative number w(e), called the weight of e. The weight of a cycle is defined as the sum of the weights of its edge...
Given an undirected graph G = (V, E) with a set V of vertices and a set E of edges, the graph coloring problem consists of partitioning all vertices into k independent sets and th...
A (k, t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total order of each vertex colour class, and a (non-proper) edge k-colouring such that between...