On graphs with a local hereditary property
نویسندگان
چکیده
منابع مشابه
On graphs with a local hereditary property
Let P be an induced hereditary property and L(P) denote the class of all graphs that satisfy the property P locally. The purpose of the present paper is to describe the minimal forbidden subgraphs of L(P) and the structure of local properties. Moreover, we prove that L(P) is irreducible for any hereditary property P. c © 2001 Elsevier Science B.V. All rights reserved.
متن کاملThe structure of almost all graphs in a hereditary property
A hereditary property of graphs is a collection of graphs which is closed under taking induced subgraphs. The speed of P is the function n 7→ |Pn|, where Pn denotes the graphs of order n in P . It was shown by Alekseev, and by Bollobás and Thomason, that if P is a hereditary property of graphs then |Pn| = 2 2/2, where r = r(P) ∈ N is the so-called ‘colouring number’ of P . However, their result...
متن کاملGraphs Having the Local Decomposition Property
Let H be a fixed graph without isolated vertices, and let G be a graph on n vertices. Let 2 ≤ k ≤ n− 1 be an integer. We prove that if k ≤ n− 2 and every k-vertex induced subgraph of G is H-decomposable then G or its complement is either a complete graph or a complete bipartite graph. This also holds for k = n − 1 if all the degrees of the vertices of H have a common factor. On the other hand, ...
متن کاملThe f-factor Problem for Graphs and the Hereditary Property
If P is a hereditary property then we show that, for the existence of a perfect f -factor, P is a sufficient condition for countable graphs and yields a sufficient condition for graphs of size א1. Further we give two examples of a hereditary property which is even necessary for the existence of a perfect f -factor. We also discuss the א2-case. We consider graphs G = (V,E), where V = V (G) is a ...
متن کاملHereditary Approximation Property
If X is a Banach space such that the isomorphism constant to `2 from n dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to `2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980 [8]. An application of the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00430-1