Even pairs in Berge graphs
نویسندگان
چکیده
Our proof (with Robertson and Thomas) of the strong perfect graph conjecture ran to 179 pages of dense matter; and the most impenetrable part was the final 55 pages, on what we called “wheel systems”. In this paper we give a replacement for those 55 pages, much easier and shorter, using “even pairs”. This is based on an approach of Maffray and Trotignon.
منابع مشابه
Even Pairs and Prism Corners in Square-Free Berge Graphs
Let G be a Berge graph such that no induced subgraph is a 4-cycle or a line-graph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair.
متن کاملEven Pairs and Prism Corners in Berge Graphs
Let G be a Berge graph such that no induced subgraph is a 4-cycle or a line-graph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair.
متن کاملBerge trigraphs
A graph is Berge if no induced subgraph of it is an odd cycle of length at least five or the complement of one. In joint work with Robertson, Seymour, and Thomas we recently proved the Strong Perfect Graph Theorem, which was a conjecture about the chromatic number of Berge graphs. The proof consisted of showing that every Berge graph either belongs to one of a few basic classes, or admits one o...
متن کاملThe Strong Perfect Graph Conjecture
A graph is perfect if, in all its induced subgraphs, the size of a largest clique is equal to the chromatic number. Examples of perfect graphs include bipartite graphs, line graphs of bipartite graphs and the complements of such graphs. These four classes of perfect graphs will be called basic. In 1960, Berge formulated two conjectures about perfect graphs, one stronger than the other. The weak...
متن کاملDecomposition of even-hole-free graphs with star cutsets and 2-joins
In this paper we consider the class of simple graphs defined by excluding, as inducedsubgraphs, even holes (i.e. chordless cycles of even length). These graphs are known aseven-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, thatuses star cutsets and 2-joins. This is a significant strengthening of the only other pre-viously known decomposition of ev...
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 99 شماره
صفحات -
تاریخ انتشار 2009