## Abstract How few edgeβdisjoint triangles can there be in a graph __G__ on __n__ vertices and in its complement $\overline {G}$? This question was posed by P. ErdΕs, who noticed that if __G__ is a disjoint union of two complete graphs of order __n__/2 then this number is __n__^2^/12β+β__o__(__n__
About triangles in a graph and its complement
β Scribed by B. Radhakrishnan Nair; A. Vijayakumar
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 338 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
In this paper, we have discussed the Nordhaus-Gaddum problems for diameter d, girth g, circumference c and edge covering number ill-We have both got the following results. If both G and G are connected, then 4<~d+a~~ 6, then p+2<.c+~<.2p, 3(p-1)<~c.~<.p 2. If both G and G have no isolated vertex, th
## Abstract For a graphb __F__ without isolated vertices, let __M__(__F__; __n__) denote the minimum number of monochromatic copies of __F__ in any 2βcoloring of the edges of __K__~__n__~. Burr and Rosta conjectured that when __F__ has order __t__, size __u__, and __a__ automorphisms. Independent
## Abstract The following is proved: If __G__ is graph of order __p__ (β₯2) and size __p__β2, then there exists an isomorphic embedding of __G__ into its complement.
Let Kr~ be the complete graph on N vertices, and assume that each edge is assigned precisly one of three possible colors. An old and difficult problem is to find the minimum number of monochromatic triangles as a function of N. We are not able to solve this problem, but we can give sharp bounds for
We show that a &-