✦ LIBER ✦

On the Parity of Colourings and Flows

✍ Scribed by Andrew J. Goodall; Dominic J.A. Welsh

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 53 KB
Volume: 84
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2084

No coin nor oath required. For personal study only.

✦ Synopsis

We extend a result of Tarsi and show that the chromatic polynomial and flow polynomial evaluated at 1+k are up to sign the same modulo k 2 for any integer k such that |k| \ 2.

📜 SIMILAR VOLUMES

On the parity of planar covers

✍ Dan Archdeacon; R. Bruce Richter 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 263 KB

## Abstract A __covering__ is a graph map ϕ: __G__ → __H__ that is an isomorphism when restricted to the star of any vertex of __G__. If __H__ is connected then |ϕ^−1^(__v__)| is constant. This constant is called the __fold number__. In this paper we prove that if __G__ is a planar graph that cover

On the Parity of Additive Representation

On the Parity of Additive Representation Functions

✍ J.-L Nicolas; I.Z Ruzsa; A Sárközy 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 334 KB

On the Parity of Exponents in the Factor

On the Parity of Exponents in the Factorization ofn!

✍ Daniel Berend 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 264 KB

It is shown that, for any k, there exist infinitely many positive integers n such that in the prime power factorization of n!, all first k primes appear to even exponents. This answers a question of Erdo s and Graham (``Old and New Problems and Results in Combinatorial Number Theory,'' L'Enseignemen

On the Number of Edges in Hypergraphs Cr

On the Number of Edges in Hypergraphs Critical with Respect to Strong Colourings

✍ Alexandr V. Kostochka; Douglas R. Woodall 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 94 KB

A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-cr

Effect of age, sex and parity on anorect

Effect of age, sex and parity on anorectal function

✍ J. S. Jameson; Y. W. Chia; Mr M. A. Kamm; C. T. M. Speakman; Y. H. Chye; M. M. H 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 388 KB

Diagonal Transformations and Cycle Parit

Diagonal Transformations and Cycle Parities of Quadrangulations on Surfaces

✍ Atsuhiro Nakamoto 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 255 KB

In this paper, we shall show that any two quadrangulations on any closed surface can be transformed into each other by diagonal slides and diagonal rotations if they have the same and sufficiently large number of vertices and if the homological properties of both quadrangulations coincide.