منابع مشابه
An Extremal Problem in Graph Theory
G(?z; I) will denote a graph of n vertices and 1 edges. Let fO(lz, K) be the smallest integer such that there is a G (n; f,, (n, k)) in which for every set of K vertices there is a vertex joined to each of these. Thus for example fO(3, 2) = 3 since in a triangle each pair of vertices is joined to a third. It can readily be checked that f,(4, 2) = 5 (the extremal graph consists of a complete 4-g...
متن کاملOn a problem in extremal graph theory
The number T*(n, k) is the least positive integer such that every graph with n = (*:I) + t vertices (t > 0) and at least T*(n, k) edges contains k mutually vertex-disjoint complete subgraphs S, , S, ,..., Sk where S, has ivertices, I < i Q k. Obviously T*(n, k) > T(n, k), the Turan number of edges for a Ki . It is shown that if n > gkk” then equality holds and that there is c :0 such that for (...
متن کاملAn Extremal Problem for Sets with Applications to Graph Theory
We prove that h<J-J:_, 1 " ;' a). This result is best possible and has some interesting consequences. Its proof uses multilinear techniques (exterior algebra).
متن کاملOn a valence problem in extremal graph theory
Let L # Kp be a p-chromatic graph and e be are edge of I, such that L e is (p IL)chromatic. If Cn is a graph of n vertices without contain&g L but containing Kp, then the minimum valence of Gn is
متن کاملOn a Valence Problem in Extremal Graph Theory P.erdös
Let L # Kp be a p-chromatic graph and e be an edge of L such that L e is (p 1)chromatic . If G n is a graph of n vertices without containing L but containing Kp , then the minimum valence of G" is 0. Notation We consider only graphs without loops and multiple edges . The number of edges, vertices and the chromatic number of a graph G will be denoted by n (1 p13/2 •) +0(1) . e(G), u(G), X(G), re...
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: Journal of the Australian Mathematical Society
سال: 1970
ISSN: 0004-9735
DOI: 10.1017/s1446788700005954