𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Note on the decomposition of λKm,n (λKm,n*) into paths

✍ Scribed by Mirosław Truszczyński

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
450 KB
Volume
55
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we investigate decompositions of a complete bipartite symmetric multidigraph ~fcL, and a complete bipartite multigraph AK," into paths of the same length. We give some necessary and/or sufficient conditions for such a decomposition to exist. We obtain also some results for the case when the paths in a decomposition need not to have equal lengths.

📜 SIMILAR VOLUMES

Decompositions of Km,n into cubes
Decompositions of Km,n into cubes
✍ Saad El-Zanati; Charles Vanden Eynden 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 384 KB

For a complete bipartite graph to be decomposable into isomorphic cubes, certain conditions on the number of cube and bipartition vertices must hold. We prove these necessary conditions sufficient in some cases. For cubes of fixed dimension d (indeed for d-regular bipartite graphs in general) we sho

A note on the equation θ̄gq = n + λΣ
A note on the equation θ̄gq = n + λΣ
✍ Shalom Eliahou; Michel Kervaire 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 565 KB

Let 0 be a cyclic difference list. We prove two theorems on the p-divisibility of the parameters of 0, where p is a prime number. The second result concerns p -2 and extends to cyclic difference lists a well known result of Turyn for cyclic difference sets. Difference lists on the cyclic group of or

On the decomposition of λK into regular
On the decomposition of λK into regular tournaments of order 5
✍ A. Mahmoodi; R. Mathon 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 558 KB

## Abstract An RTD[5,λ; __v__] is a decomposition of the complete symmetric directed multigraph, denoted by λK, into regular tournaments of order 5. In this article we show that an RTD[5,λ; __v__] exists if and only if (__v__−1)λ ≡ 0 (mod 2) and __v__(__v__−1)λ ≡ 0 (mod 10), except for the impossib

On the number of spanning trees of Kn an
On the number of spanning trees of Kn and Km, n
✍ Moh'd Z. Abu-Sbeih 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 170 KB

The object of this paper is to introduce a new technique for showing that the number of labelled spanning trees of the complete bipartite graph K,,,, is IT(m, n)l = m"-'n"-'. As an application, we use this technique to give a new proof of Cayley's formula IT(n)1 = nnm2, for the number of labelled s