The r-covered property of the line graphs
Daqing Yang · Fuzhou daxue xuebao. Ziran kexue ban · 2005
Let G be a graph. Let L(G) denote the line graph of G. A graph G is r-covered if each edge of G belongs to a r-factor of G. We show the following results: Suppose m≥2 is an even integer. If d_G(v)≥m+1 for all v∈V(G), then L(G) is 2m-covered. Suppose m is a positive integer, and G is a connected graph with E(G) even. If d_G(v)≥m+3 for all v∈V(G), then L(G) is (2m+1)-covered.