Claw-free graphs. V. Global structure
نویسندگان
چکیده
A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In earlier papers of this series we proved that every claw-free graph either belongs to one of several basic classes that we described explicitly, or admits one of a few kinds of decomposition. In this paper we convert this “decomposition” theorem into a theorem describing the global structure of claw-free graphs.
منابع مشابه
Finding a smallest odd hole in a claw-free graph using global structure
A lemma of Fouquet implies that a claw-free graph contains an induced C5, contains no odd hole, or is quasi-line. In this paper we use this result to give an improved shortest-oddhole algorithm for claw-free graphs by exploiting the structural relationship between line graphs and quasi-line graphs suggested by Chudnovsky and Seymour’s structure theorem for quasi-line graphs. Our approach involv...
متن کاملClaw-free graphs. III. Circular interval graphs
Construct a graph as follows. Take a circle, and a collection of intervals from it, no three of which have union the entire circle; take a finite set of points V from the circle; and make a graph with vertex set V in which two vertices are adjacent if they both belong to one of the intervals. Such graphs are “circular interval graphs”, and they form an important subclass of the class of all cla...
متن کاملClaw-free graphs. VII. Quasi-line graphs
A graph is a quasi-line graph if for every vertex v, the set of neighbours of v is expressible as the union of two cliques. Such graphs are more general than line graphs, but less general than claw-free graphs. Here we give a construction for all quasi-line graphs; it turns out that there are basically two kinds of connected quasi-line graphs, one a generalization of line graphs, and the other ...
متن کاملHamiltonicity in Partly claw-free graphs
Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n − 2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such th...
متن کاملThe Structure of Claw-Free Perfect Graphs
In 1988, Chvátal and Sbihi [4] proved a decomposition theorem for claw-free perfect graphs. They showed that claw-free perfect graphs either have a clique-cutset or come from two basic classes of graphs called elementary and peculiar graphs. In 1999, Maffray and Reed [6] successfully described how elementary graphs can be built using line-graphs of bipartite graphs using local augmentation. How...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 98 شماره
صفحات -
تاریخ انتشار 2008