The edge-coloring of almost-outerplanar graphs
Huimin Song · Journal of Shandong University · 2004
If a graph G has an edge e such that G-e is outerplanar,then G is called almost-outerplanar graph. In this paper,we prove that a connected almost-outerplanar graph G has the edge chromatic number Δ(G)+ 1 if and only if G is an odd cycle,or Δ(G )=3 and G has a 2-connected subgraph which contains a unique 2-vertex. It generalizes a result of Fiorinis'.