ON SOME NEW INEQUALITIES CONCERNING EXTREMAL PROPERTIES OF GRAPHS by
ON SOME NEW INEQUALITIES CONCERNING EXTREMAL PROPERTIES OF GRAPHS by
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发表时间：
2004
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通讯作者：
I. Elldős
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作者：
I. Elldős
Denote by G(n; 1) a graph of 'n vertices and l edges . x(G) will denote the ( ,hromattc number of G . K,.(p,, . . ., p,) denotes the complete r-chromatic graph with p i vertices of the i-th colourwhere any two vertices of different colour are joined . K,(p) is a graph consisting of p isolated vertices . ( ' : K,(p„ . . ., p,)) is obtained from G by adjoining a K_,(p ,, . . ., p,), and b joining every new vertex to all the vertices of C . Clearly ;((G : K,(pv . . . . p,))= (G) + r,f(n ; G) is the smallest integer so that every G,(n ; f(n; G)) contains Gas a subgraph . The graphs G'()?,) =G'(n; f(n; G) 1) which (lo not contain G as a subgraph are called the extremal graphs belonging to G . The vertices of G will be denoted by x, x,, . . ., y, . . ., the edges will be denoted by (x, y) . The valence of a vertex x of G is the number of edges incident to x . -r(G) denotes the number of vertices, v(G) the number of edges of'G. If G' is graph and x„ . . ., x,,. are some of'the vortices of G' then G'(x,, . . . . x,;) is the suhuraph 4 6" spanned by x,, . . ., x,; . C, c" . . . denote absolute constants not necessarily the same if' they occur in different fornua1as . In a previous paper [ 1 I 1 stated without proof that
