A tree T is said to be bad, if it is the vertex-disjoint union of two stars plus an edge joining the center of the first star to an end-vertex of the second star. A tree T is good, if it is not bad. In this article, we prove a conjecture of Alan Hartman that, for any spanning tree T of K 2m , where
On a conjecture of Aris: Proof and remarks
โ Scribed by Dan Luss; Neal R. Amundson
- Publisher
- American Institute of Chemical Engineers
- Year
- 1967
- Tongue
- English
- Weight
- 428 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0001-1541
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k โฅ 2, there exists . This conjecture is also verified for k = 2, 3 in [Wang, to appear; Wang, manuscript]. In this article, we prove this conjecture to be true if n โฅ 3k, i.e., M (k) โค 3k. W
Let the square of a tournament be the digraph on the same nodes with arcs where the directed distance in the tournament is at most two. This paper verifies Dean's conjecture: any tournament has a node whose outdegree is at least doubled in its square. 0
This article is motivated by a conjecture of Thomassen and Toft on the number s 2 (G) of separating vertex sets of cardinality 2 and the number v 2 (G) of vertices of degree 2 in a graph G belonging to the class G of all 2-connected graphs without nonseparating induced cycles. Let G denote the numbe