Asymptotic Structure of Graphs with the Minimum Number of Triangles

نویسندگان

  • Oleg Pikhurko
  • Alexander A. Razborov
چکیده

We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that minimize the triangle density.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Tensor Product of Graphs, Girth and Triangles

The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

متن کامل

Some finite groups with divisibility graph containing no triangles

Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...

متن کامل

Minimum Tenacity of Toroidal graphs

The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...

متن کامل

Monochromatic triangles in three-coloured graphs

In 1959, Goodman [9] determined the minimum number of monochromatic triangles in a complete graph whose edge set is 2-coloured. Goodman [10] also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours. In this paper, for n sufficiently large, we determine the minimum number of monochromatic triangles in a 3-coloured copy of K...

متن کامل

Some Results on the Maximal 2-Rainbow Domination Number in Graphs

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Combinatorics, Probability & Computing

دوره 26  شماره 

صفحات  -

تاریخ انتشار 2017