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Planar graphs of oddgirth at least 9 are homomorphic to Petersen graph
"... Let G be a graph and let c: V (G) → � {1,...,5} � 2 be an assignment of 2element subsets of the set {1,...,5} to the vertices of G such that for every edge vw, the sets c(v) and c(w) are disjoint. We call such an assignment a (5,2)coloring. A graph is (5,2)colorable if and only if it has a homo ..."
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Cited by 4 (1 self)
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homomorphism to the Petersen graph. The oddgirth of a graph G is the length of the shortest odd cycle in G ( ∞ if G is bipartite). We prove that every planar graph of oddgirth at least 9 is (5,2)colorable, and thus it is homomorphic to the Petersen graph. Also, this implies that such graphs have fractional
Circular Chromatic Number of Planar Graphs of Large Odd Girth
, 2001
"... It was conjectured by Jaeger that 4kedge connected graphs admit a (2k + 1; k)ow. 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& ..."
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's conjecture is largely open. The k = 1 case is the wellknown Grotzsch 3colour theorem. This paper proves that for k 2, planar graphs of odd girth at least 8k 3 have circular chromatic number at most 2 + 1 k . 1
Increasing chromatic number and girth
, 2012
"... This expository paper deals with some interesting concepts related to the problem of increasing the chromatic number and the girth of a graph. Specifically, the proof of Kneserâs conjecture and also related concepts such as Galeâs distribution of points on the sphere and the Borsuk graph will b ..."
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This expository paper deals with some interesting concepts related to the problem of increasing the chromatic number and the girth of a graph. Specifically, the proof of Kneserâs conjecture and also related concepts such as Galeâs distribution of points on the sphere and the Borsuk graph
GIRTH AND CHROMATIC NUMBER OF GRAPHS
"... Abstract. This paper will look at the relationship between high girth and high chromatic number in both its finite and transfinite incarnations. On the one hand, we will demonstrate that it is possible to construct graphs with high oddgirth and high chromatic number in all cases. We will then look a ..."
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Abstract. This paper will look at the relationship between high girth and high chromatic number in both its finite and transfinite incarnations. On the one hand, we will demonstrate that it is possible to construct graphs with high oddgirth and high chromatic number in all cases. We will then look
Codes and Decoding on General Graphs
, 1996
"... Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithm ..."
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Cited by 359 (1 self)
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algorithms are special cases of two generic algorithms, the minsum and sumproduct algorithms, which also include noniterative algorithms such as Viterbi decoding. The minsum and sumproduct algorithms are developed and presented as generalized trellis algorithms, where the time axis of the trellis
A NOTE ON CIRCULAR CHROMATIC NUMBER OF GRAPHS WITH LARGE GIRTH AND SIMILAR PROBLEMS
"... Abstract. In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite. We also prove a similar result for the oriented chromatic number, from which follows in particular that graphs of large girth excluding ..."
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Abstract. In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite. We also prove a similar result for the oriented chromatic number, from which follows in particular that graphs of large girth excluding
Circular Flow and Circular Chromatic Number . . .
, 2007
"... This thesis considers circular flowtype and circular chromatictype parameters (φ and χ, respectively) for matroids. In particular we focus on orientable matroids and 6√1matroids. These parameters are obtained via two approaches: algebraic and orientationbased. The general questions we discuss ..."
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This thesis considers circular flowtype and circular chromatictype parameters (φ and χ, respectively) for matroids. In particular we focus on orientable matroids and 6√1matroids. These parameters are obtained via two approaches: algebraic and orientationbased. The general questions we discuss
On generalizations of the Petersen graph and the Coxeter graph
"... In this note we consider two related infinite families of graphs, which generalize the Petersen and the Coxeter graph. The main result proves that these graphs are cores. It is determined which of these graphs are vertex/edge/arctransitive or distanceregular. Girths and odd girths are computed. A ..."
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In this note we consider two related infinite families of graphs, which generalize the Petersen and the Coxeter graph. The main result proves that these graphs are cores. It is determined which of these graphs are vertex/edge/arctransitive or distanceregular. Girths and odd girths are computed. A
PROBLEMS AND RESULTS ON 3CHROMATIC HYPERGRAPHS AND SOME RELATED QUESTIONS
 COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 10. INFINITE AND FINITE SETS, KESZTHELY (HUNGARY)
, 1973
"... A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph i ..."
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Cited by 317 (0 self)
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is simple if any two edges have at most one common point, and it is called a clique if any two edges have at least one common point. The chromatic number of a hypergraph is the least number k such that the points can be kcolored so that no edge is monochromatic. As far as we know families of sets
Circular chromatic number and graph minor
, 2000
"... This paper proves that for any integer n ≥ 4 and any rational number r, 2 ≤ r ≤ n − 2, there exists a graph G which has circular chromatic number r and which does not contain Kn as a minor. ..."
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Cited by 1 (1 self)
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This paper proves that for any integer n ≥ 4 and any rational number r, 2 ≤ r ≤ n − 2, there exists a graph G which has circular chromatic number r and which does not contain Kn as a minor.
Results 1  10
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