The Erdös-Hajnal conjecture for bull-free graphs
نویسندگان
چکیده
The bull is a graph consisting of a triangle and two pendant edges. A graphs is called bull-free if no induced subgraph of it is a bull. In this paper we prove that every bull-free graph on n vertices contains either a clique or a stable set of size n 1 4 , thus settling the Erdős-Hajnal conjecture [5] for the bull.
منابع مشابه
The structure of bull-free graphs I - Three-edge-paths with centers and anticenters
The bull is the graph consisting of a triangle and two disjoint pendant edges. A graph is called bull-free if no induced subgraph of it is a bull. This is the first paper in a series of three. The goal of the series is to explicitly describe the structure of all bull-free graphs. In this paper we study the structure of bull-free graphs that contain as induced subgraphs three-edge-paths P and Q,...
متن کاملErdös-Gyárfás Conjecture for Cubic Planar Graphs
In 1995, Paul Erdős and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.
متن کاملProof of a Conjecture of Mader, Erdös and Hajnal on Topological Complete Subgraphs
A topological complete graph of order p comprises p vertices {v1, . . . , vp} and (p 2 ) pairwise vertex disjoint paths Pi, j , 1 ≤ i < j ≤ p, such that Pi, j joins vi to v j . It was conjectured by Mader [11], and also by Erdös and Hajnal [6], that there is a positive constant c such that any graph G of size at least cp2|G| contains a topological complete subgraph of order p. It was pointed ou...
متن کاملThe Erdös-Hajnal Conjecture - A Survey
The Erdös-Hajnal conjecture states that for every graph H, there exists a constant δ(H) > 0 such that every graph G with no induced subgraph isomorphic to H has either a clique or a stable set of size at least |V (G)|. This paper is a survey of some of the known results on this conjecture.
متن کاملErdös-Hajnal Conjecture for Graphs with Bounded VC-Dimension
The Vapnik-Chervonenkis dimension (in short, VC-dimension) of a graph is defined as the VCdimension of the set system induced by the neighborhoods of its vertices. We show that every n-vertex graph with bounded VC-dimension contains a clique or an independent set of size at least e(logn) . The dependence on the VC-dimension is hidden in the o(1) term. This improves the general lower bound, e √ ...
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