On the sum of the reciprocals of cycle lengths in sparse graphs
نویسندگان
چکیده
and Hajnal [I] introduced the real function f(a) =inf {.P(G) J ~~i~: ~a}. They asked about the behaviour ofj(rx) as rx tends to infinity. The complete bipartite graph Kn,n shows that f(n)~c ·log n for n~2, but originally it was unknown whether f(a) is bouJ1ded or not. Recently Gyarfas, Koml6s and Szemeredi (2] showed that f(a) ~a ·log a, provided that a>b, where a and bare suitable contants. Obviously f(a)=O for rx~ 1. The problem of determining the behaviour ofj(rx) for aE(l, 1 +e) has been raised in [2]. It was not even clear whether f(l +e) >0 for every e >0. In this paper we prove the following theorem, answering this question in the affirmative: '
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ورودعنوان ژورنال:
- Combinatorica
دوره 5 شماره
صفحات -
تاریخ انتشار 1985