a circle. Chudnovsky and Seymour classify arbitrary connected claw-free graphs into one of the following: Six specific subclasses of claw-free graphs. Three of these are line graphs, proper circular arc graphs, and the induced subgraphs of an icosahedron; the other three involve additional definitions. Graphs formed in four simple ways from smaller claw-free graphs. Antiprismatic graphs, a class of dense graphs defined as the claw-free graphs in which every four vertices induce a subgraph with at least two edges. Much of the work in their structure theory involves a further analysis of antiprismatic graphs. The Schläfli graph, a claw-free strongly regular graph with parameters srg(27,16,10,8), plays an important role in this part of the analysis. This structure theory has led to new advances in polyhedral combinatorics and new bounds on the chromatic number of claw-free graphs, as well as to new fixed-parameter-tractable algorithms for dominating sets in claw-free graphs. Notes References . . . . . . . . . . . . . . . . . . . . . . . External links Claw-free graphs, Information System on Graph Class Inclusions Graph families Matching (graph theory)