TY - JOUR

T1 - Extremal Problems Concerning Transformations of the Set of Edges of the Complete Graph

AU - Alon, N.

AU - Caro, Y.

PY - 1986

Y1 - 1986

N2 - Let Em denote the set of edges of the complete graph on m vertices Km, and let f : Em → Em be a function. A subgraph G = (V (G), E (G)) of Km is called f-fixed if f(e) = e for all e ∈ E (G) and f-free if f(e) ∉ E(G) for all e ∈ E(G). For two finite graphs G, H we define m(G,H)=max{m:∃f:Em→EmsuchthatnocopyofGinKmisf-fixedandnocopyofHinKmisf-free} If m > 2 we define l(m,H)=max{l:∃f:Em→Em,f(e)≠eforledgese∈EmandnocopyofHinKmisf-free} In this paper we investigate the functions m(G, H) and l(m, H). We determine m(G, H) precisely for some families of graphs and estimate the asymptotic behaviour of l(m, H) for fixed H as m tends to infinity. Some of the results are generalised to functions defined on the set of edges of a hypergraph.

AB - Let Em denote the set of edges of the complete graph on m vertices Km, and let f : Em → Em be a function. A subgraph G = (V (G), E (G)) of Km is called f-fixed if f(e) = e for all e ∈ E (G) and f-free if f(e) ∉ E(G) for all e ∈ E(G). For two finite graphs G, H we define m(G,H)=max{m:∃f:Em→EmsuchthatnocopyofGinKmisf-fixedandnocopyofHinKmisf-free} If m > 2 we define l(m,H)=max{l:∃f:Em→Em,f(e)≠eforledgese∈EmandnocopyofHinKmisf-free} In this paper we investigate the functions m(G, H) and l(m, H). We determine m(G, H) precisely for some families of graphs and estimate the asymptotic behaviour of l(m, H) for fixed H as m tends to infinity. Some of the results are generalised to functions defined on the set of edges of a hypergraph.

UR - http://www.scopus.com/inward/record.url?scp=84991563996&partnerID=8YFLogxK

U2 - 10.1016/S0195-6698(86)80034-8

DO - 10.1016/S0195-6698(86)80034-8

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AN - SCOPUS:84991563996

SN - 0195-6698

VL - 7

SP - 93

EP - 104

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 2

ER -