Dense Graphs With a Large Triangle Cover Have a Large Triangle Packing

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Dense Graphs With a Large Triangle Cover Have a Large Triangle Packing

It is well known that a graph with m edges can be made triangle-free by removing (slightly less than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make triangle-free in the sense that it is necessary to remove roughly m/2 edges in order to eliminate all triangles. We prove that dense graphs that are hard to make triangle-free have a large packing of pairwise ...

متن کامل

Large Cuts with Local Algorithms on Triangle-Free Graphs

We study the problem of finding large cuts in d-regular triangle-free graphs. In prior work, Shearer (1992) gives a randomised algorithm that finds a cut of expected size (1/2 + 0.177/ √ d)m, where m is the number of edges. We give a simpler algorithm that does much better: it finds a cut of expected size (1/2 + 0.28125/ √ d)m. As a corollary, this shows that in any d-regular triangle-free grap...

متن کامل

Triangle-free geometric intersection graphs with large chromatic number

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set X in R that is not an axis-aligned rectangle and for any pos...

متن کامل

Triangle-Free Geometric Intersection Graphs with No Large Independent Sets

It is proved that there are triangle-free intersection graphs of line segments in the plane with arbitrarily small ratio between the maximum size of an independent set and the total number of vertices.

متن کامل

Sparse halves in dense triangle-free graphs

In this paper we study the conjecture that any triangle-free graph G on n vertices should contain a set of bn/2c vertices that spans at most n2/50 edges. This problem was considered by Erdős, Faudree, Rousseau and Schelp in [5]. Krivelevich proved the conjecture for graphs with minimum degree at least 2 5n [8]. In [7] Keevash and Sudakov improved this result to graphs with average degree at lea...

متن کامل

ذخیره 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: Combinatorics, Probability and Computing

سال: 2012

ISSN: 0963-5483,1469-2163

DOI: 10.1017/s0963548312000235