Interval edge colorings of some products of graphs

Abstract

An edge co汯r楮g of a graph G w楴h co汯rs 1 ,2,...,t 楳 ca汬ed an 楮terval t-co汯r楮g 楦 for each i 2 f1,2,...,tg there 楳 at 汥ast one edge of G co汯red by i, and the co汯rs of edges 楮c楤ent to any vertex of G are d楳t楮ct and form an 楮terval of 楮tegers. A graph G 楳 楮terval co汯rab汥, 楦 there 楳 an 楮teger t � 1 for wh楣h G has an 楮terval t-co汯r楮g. Let N be the set of a汬 楮terval co汯rab汥 graphs. In 2004 Kuba汥 and G楡ro showed that 楦 G,H 2 N, then the Cartes楡n product of these graphs be汯ngs to N. A汳o, they formu污ted a s業楬ar prob汥m