✦ LIBER ✦

Colouring finite planes of odd order

✍ Scribed by J Csima

Publisher: Elsevier Science
Year: 1984
Tongue: English
Weight: 40 KB
Volume: 49
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90168-7

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that in every n-coiouring ((n -1)-colouring) of a projective plane (affme plane) of odd order n at least one line has three points of the same colour.

Using clever counting arguments, Kabell proves that "In any n-coloring of PG(2, n), at least one line contains points of at most n-1 colors." and that "In any (n -1)-coloring of AG(2, n), at least one line contains points of at most n -2 colors." In this note we give a pair of stronger theorems for planes of odd order.

📜 SIMILAR VOLUMES

Finite Laguerre Near-planes of Odd Order

Finite Laguerre Near-planes of Odd Order Admitting Desarguesian Derivations

✍ Günter F. Steinke 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 147 KB

We introduce finite Laguerre near-planes and investigate such planes of odd order that admit a Desarguesian derivation.

I-Transitive Ovals in Projective Planes

I-Transitive Ovals in Projective Planes of Odd Order

✍ Maria Rosaria Enea; Gábor Korchmáros 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 202 KB

Let be a projective plane of odd order n containing an oval ⍀. We give a classification of collineation groups of which fix ⍀ and act transitively on the set I I of all internal points of ⍀.

On Finite s-Transitive Graphs of Odd Ord

On Finite s-Transitive Graphs of Odd Order

✍ Cai Heng Li 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 128 KB

It is shown that, for a positive integer s, there exists an s-transitive graph of odd order if and only if s 3 and that, for s=2 or 3, an s-transitive graph of odd order is a normal cover of a graph for which there is an automorphism group that is almost simple and s-transitive.

Equivariant Witt groups of finite groups

Equivariant Witt groups of finite groups of odd order

✍ Masahiko Miyamoto 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 842 KB

On finite groups of odd order admitting

On finite groups of odd order admitting involutory automorphisms

✍ H Matsuyama 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 326 KB

On the Non-existence of Thas Maximal Arc

On the Non-existence of Thas Maximal Arcs in Odd Order Projective Planes

✍ A. Blokhuis; N. Hamilton; H. Wilbrink 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 91 KB

In this paper it is shown that given a non-degenerate elliptic quadric in the projective space PG(2n -1, q), q odd, then there does not exist a spread of PG(2n -1, q) such that each element of the spread meets the quadric in a maximal totally singular subspace. An immediate consequence is that the c