An Erdős-Stone Type Conjecture for Graphic Sequences
نویسندگان
چکیده
منابع مشابه
An Erdös-Stone Type Conjecture for Graphic Sequences
We consider a variation of the classical Turán-type extremal problem as introduced by Erdős, Jacobson and Lehel in [4]. Let π be an n-element graphic sequence and let H be a graph. We wish to determine the smallest even integer m such that any n-term graphic sequence π having degree sum at least m has some realization containing H as a subgraph. Denote this value m by σ(H,n). For an arbitrarily...
متن کاملImproved bounds for Erdős' Matching Conjecture
Article history: Received 7 June 2012 Available online 24 February 2013
متن کاملThe Erdős-Hajnal conjecture for rainbow triangles
We prove that every 3-coloring of the edges of the complete graph on n vertices without a rainbow triangle contains a set of order Ω ( n log n ) which uses at most two colors, and this bound is tight up to a constant factor. This verifies a conjecture of Hajnal which is a case of the multicolor generalization of the well-known Erdős-Hajnal conjecture. We further establish a generalization of th...
متن کاملThe Erdős-Sós Conjecture for Geometric Graphs
Let f(n, k) be the minimum number of edges that must be removed from some complete geometric graph G on n points, so that there exists a tree on k vertices that is no longer a planar subgraph of G. In this paper we show that 1 2 n k 1 n 2 f(n, k) 2 n(n 2) k 2 . For the case when k = n, we show that 2 f(n, n) 3. For the case when k = n and G is a geometric graph on a set of points in con...
متن کاملAdjusting a conjecture of Erdős
We investigate a conjecture of Paul Erdős, the last unsolved problem among those proposed in his landmark paper [2]. The conjecture states that there exists an absolute constant C > 0 such that, if v1, . . . , vn are unit vectors in a Hilbert space, then at least C 2 n of all ∈ {−1, 1} are such that | Pn i=1 ivi |≤ 1. We disprove the conjecture. For Hilbert spaces of dimension d > 2, the counte...
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: Electronic Notes in Discrete Mathematics
سال: 2007
ISSN: 1571-0653
DOI: 10.1016/j.endm.2007.01.018