Weak diameter coloring of graphs on surfaces

A weak-dynamic coloring of a graph is a vertex coloring (not necessarily proper) in such a way that each vertex of degree at least two sees at least two colors in its neighborhood. It is proved that the weak-dynamic chromatic number of the class ...${}_{\mathrm{}}$$\mathrm{}$

A graph G is equimatchable if each matching in G is a subset of a maximum-size matching and it is factor critical if G-v has a perfect matching for each vertex v of G. It is known that any 2-connected equimatchable graph is either bipartite or factor ...

The domination number of a graph G, denoted by $$\gamma (G)$$?(G), is the minimum cardinality of a dominating set of G. A vertex of a graph is called critical if its deletion decreases the domination number, and a graph is called critical if its all ...