منابع مشابه
Cycles with consecutive odd lengths
In this paper we prove that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence of the absolute constant d > 0 that every non-bipartite 2-connected graph with minimum degree at least dk contains cycles of all lengths modulo k,...
متن کاملColourings of graphs with two consecutive odd cycle lengths
In 1992 Gyárfás showed that a graph G having only k odd cycle lengths is (2k + 1)colourable, if it does not contain a K2k+2. In this paper, we will present the results for graphs containing only odd cycles of length 2m − 1 and 2m + 1 as done in [S. Matos Camacho, Colourings of graph with prescribed cycle lengths, diploma thesis, TU Bergakademie Freiberg, 2006. [3]]. We will show that these grap...
متن کاملGraphs with k odd cycle lengths
Gyarfas, A., Graphs with k odd cycle lengths, Discrete Mathematics 103 (1992) 41-48. 41 If G is a graph with k ~ 1 odd cycle lengths then each block of G is either K2k+Z or contains a vertex of degree at most 2k. As a consequence, the chromatic number of G is at most 2k + 2. For a graph G let L(G) denote the set of odd cycle lengths of G, i.e., L( G) = {2i + 1: G contains a cycle of length 2i +...
متن کاملIdentifying codes of cycles with odd orders
The problem of the r -identifying code of a cycle Cn has been solved totally when n is even. Recently, S. Gravier et al. give the r -identifying code for the cycle Cn with the minimum cardinality for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) 6= 1. In this paper, we deal with the r -identifying code of the cycle Cn for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) = 1. c © 2007 Elsevier Ltd. All rig...
متن کاملOn Lengths of Rainbow Cycles
We prove several results regarding edge-colored complete graphs and rainbow cycles, cycles with no color appearing on more than one edge. We settle a question posed by Ball, Pultr, and Vojtěchovský [BPV05] by showing that if such a coloring does not contain a rainbow cycle of length n, where n is odd, then it also does not contain a rainbow cycle of length m for all m greater than 2n. In additi...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2016
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2015.09.002