The forcing star edge chromatic number of a graph

Abstract

Let S be a χ’_st-set of G. A subset T⊆S is called a forcing subset for S if S is the unique χ’_st-set containing T. The forcing star-edge chromatic number χ’_st(S) of S in G is the minimum cardinality of a forcing subset for S. The forcing star-edge chromatic number χ’_st(G) of G is the smallest forcing number of all χ’_st-sets of G. Some general properties satisfied by this concept are studied. It is shown that for every pair a and b of integers with 0≤a<b and b>a+2 there exists a connected graph G such that χ’_st(G)=a and χ’_st(G)=b, where χ’_st(G) is the star edge chromatic number of a graph.