منابع مشابه
Circular Chromatic Number of Planar Graphs of Large Odd Girth
It was conjectured by Jaeger that 4k-edge connected graphs admit a (2k + 1, k)-flow. The restriction of this conjecture to planar graphs is equivalent to the statement that planar graphs of girth at least 4k have circular chromatic number at most 2 + 1 k . Even this restricted version of Jaeger’s conjecture is largely open. The k = 1 case is the well-known Grötzsch 3-colour theorem. This paper ...
متن کاملGraphs With Large Girth And Large Chromatic Number
In the first part of these notes we use a probabilistic method to show the existence of graphs with large girth and large chromatic number. In the second part we give an explicit example of such graphs. It is mostly based on the third chapter of Some Applications Of Modular Forms by Peter Sarnak and also the third and forth chapters of Elementary Number Theory, Group Theory, And Ramanujan Graph...
متن کاملn-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 2k1 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 کاملThe Independence Number of Graphs with Large Odd Girth
Let G be an r-regular graph of order n and independence number α(G). We show that if G has odd girth 2k + 3 then α(G) ≥ n1−1/kr1/k . We also prove similar results for graphs which are not regular. Using these results we improve on the lower bound of Monien and Speckenmeyer, for the independence number of a graph of order n and odd girth 2k + 3. AMS Subject Classification. 05C15 §
متن کامل(2 + ϵ)-Coloring of planar graphs with large odd-girth
The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f( ), then G is (2 + )-colorable. Note that the function f( ) is independent of the graph G and → 0 if and only if f( )→∞. A key lemma...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00221-4