DEFICIENCY OF OUTERPLANAR GRAPHS - Khachatryan, H.H. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2017)
An edge-coloring of a graph G with colors 1,2,...,t is an interval t-coloring, if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable, if it has an interval t-coloring for some positive integer t. def (G) denotes the minimum number of pendant edges that should be attached to G to make it interval colorable. In this paper we study interval colorings of outerplanar graphs. In particular, we show that if G is an outerplanar graph, then def(G) ≤ (|V(G)|-2)/(og(G)-2), where og(G) is the length of the shortest cycle with odd number of edges in G.