Edge-Face Coloring of Plane Graphs with Maximum Degree Nine

An acyclic edge coloring of a graph G is a proper edge coloring with an additional condition that any pair of colors induces a linear forest (an acyclic graph with maximum degree

We show an upper bound for the maximum vertex degree of any z-oblique graph imbedded into a given surface.. Moreover, an upper bound for the maximum face degree

One common notion of graph theory is the one of proper edge-coloring, which is, given an undirected simple graph G = (V, E), an assignment of colors to the edges such that no

We show that any graph of maximum degree ∆ has acyclic chromatic number at most ∆(∆−1) 2 for any ∆ ≥ 5, and we give an O(n∆ 2 ) algorithm to acyclically color any graph

This question seems to be more intriguing, since as we remarked so far, the graph having the maximum average degree strictly smaller than 20 7 and needing nine colours to be strong

A proper vertex colouring of a graph G is 2-frugal (resp. linear) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths)..

An (α,β)-maximal bichromatic path with respect to a partial edge- colouring c of G is a maximal path consisting of edges that are coloured using the colours α and β alternatingly..

The facial parity edge colouring of a connected bridgeless plane graph is such an edge colouring in which no two face-adjacent edges (consecutive edges of a facial walk of some