The maximum matching extendability and factor-criticality of 1-planar graphs

A graph is 1-planar if it can be drawn in the sphere or plane so that any edge has at most one crossing point with another edge. It known a G least three vertices contains 4|V(G)|−8 edges, optimal exactly edges. Fujisawa et al. (2018) first considered matching extension of graphs, obtained each even order 1-extendable and characterized 2-extendable graphs 3-matchings extendable to perfect matchings as well. In this short paper, we prove no 3-extendable. Further mainly obtain 5-extendable by discharge method also construct 4-extendable graph. Finally get 7-factor-critical 6-factor-critical.