COLORING PROBLEM OF SIGNED INTERVAL GRAPHS

We consider simple graphs g = (v, e), i.e graphs without loops and multiple edges. a graph g together with a function s : e −→ {+, −} on the edge set of g is called a signed graph. if σ is the set of edges whose image under s is ” − ”, then we denote the signed graph by σ = (g, σ). the graph g is called the ground of σ and the set σ is called the signature of it. for any edge e of σ, we call it a positive or negative edge if s(e) has positive or negative sign respectively. by the edge and vertex set of σ we mean those of the ground graph that are v, e respectively. for a signed graph σ = (g, σ) by the positive (negative ) subgraph we mean the spanning subgraph of g where the edge set is the set of positive (negative) edges of σ and is denoted by σ+ (σ−).