It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct… (More)

A rainbow path in an edge coloured graph is a path in which no two edges are coloured the same. A rainbow colouring of a connected graph G is a colouring of the edges of G such that every pair of… (More)

A Weight graph is a connected (multi)graph with two vertices u and v of degree at least three and other vertices of degree two. Moreover, if any of these two vertices is removed, the remaining graph… (More)

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective,… (More)

A Theta graph is a multigraph which is a union of at least three internally disjoint paths that have the same two distinct end vertices. We show full computational complexity characterization of the… (More)

A covering projection from a graph G to a graph H is a mapping of the vertices of G to the vertices of H such that, for every vertex v of G, the neighborhood of v is mapped bijectively to the… (More)

A homomorphism from a graph G to a graph H is locally bijective, injective, or surjective if its restriction to the neighborhood of every vertex of G is bijective, injective, or surjective,… (More)

We show that the problem whether a given simple graph G admits a quasi-covering to a fixed connected graph H is solvable in polynomial time if H has at most two vertices and that it is NP-complete… (More)