A note on n-tuple colourings and circular colourings of planar graphs with large odd girth

نویسندگان

  • Petra Sparl
  • Janez Zerovnik
چکیده

International Journal of Computer Mathematics Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713455451 A note on n-tuple colourings and circular colourings of planar graphs with large odd girth P. šparl ab; J. žerovnik ac a IMFM, Slovenia b FG, University of Maribor, Slovenia c FS, University of Maribor, Slovenia

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Frugal Colouring of Graphs

A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring was introduced by Hind, Molloy and Reed in 1997. In this paper, we study the frugal chromatic number of planar graphs, planar graphs with large girth, and outerplanar graphs, and relate this parameter with several wel...

متن کامل

Homomorphism bounds and edge-colourings of K4-minor-free graphs

We present a necessary and sufficient condition for a graph of odd-girth 2k + 1 to bound the class of K4-minor-free graphs of odd-girth (at least) 2k + 1, that is, to admit a homomorphism from any such K4-minor-free graph. This yields a polynomial-time algorithm to recognize such bounds. Using this condition, we first prove that every K4-minor free graph of odd-girth 2k+1 admits a homomorphism ...

متن کامل

Homomorphisms and edge-colourings of planar graphs

We conjecture that every planar graph of odd-girth 2k + 1 admits a homomorphism to Cayley graph C(Z 2 , S2k+1), with S2k+1 being the set of (2k + 1)vectors with exactly two consecutive 1’s in a cyclic order. This is an strengthening of a conjecture of T. Marshall, J. Nešetřil and the author. Our main result is to show that this conjecture is equivalent to the corresponding case of a conjecture ...

متن کامل

n-Tuple Coloring of Planar Graphs with Large Odd Girth

The main result of the papzer is that any planar graph with odd girth at least 10k À 7 has a homomorphism to the Kneser graph G 2k‡1 k , i.e. each vertex can be colored with k colors from the set f1; 2;. .. ; 2k ‡ 1g so that adjacent vertices have no colors in common. Thus, for example, if the odd girth of a planar graph is at least 13, then the graph has a homomorphism to G 5 2 , also known as...

متن کامل

Randomly Colouring Graphs with Girth Five and Large Maximum Degree

We prove that the Glauber dynamics on the k-colourings of a graph G on n vertices with girth 5 and maximum degree ∆ ≥ 1000 log n mixes rapidly if k = q∆ and q > β where β = 1.645... is the root of 2− (1− e−1/β)2 − 2βe−1/β = 0.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Int. J. Comput. Math.

دوره 84  شماره 

صفحات  -

تاریخ انتشار 2007