Relations To Other Families of Graphs
Every line graph is a claw-free graph. Some of the properties of claw-free graphs are generalizations of those of line graphs.
The line graph of a bipartite graph is perfect (see König's theorem). The line graphs of bipartite graphs form one of the key building blocks of perfect graphs, used in the proof of the perfect graph theorem. A special case is the rook's graphs, line graphs of complete bipartite graphs.
Read more about this topic: Line Graph
Famous quotes containing the words relations and/or families:
“In the mythic schema of all relations between men and women, man proposes, and woman is disposed of.”
—Angela Carter (1940–1992)
“Accidents will occur in the best-regulated families; and in families not regulated by that pervading influence which sanctifies while it enhances ... in short, by the influence of Woman, in the lofty character of Wife, they may be expected with confidence, and must be borne with philosophy.”
—Charles Dickens (1812–1870)