منابع مشابه
Graphs 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 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 Odd Cycle Lengths 5 and 7 are 3-Colorable
Let L(G) denote the set of all odd cycle lengths of a graph G. Gyárfás gave an upper bound for χ(G) depending on the size of this set: if |L(G)| = k ≥ 1, then χ(G) ≤ 2k+1 unless some block of G is a K2k+2, in which case χ(G) = 2k+2. This bound is generally tight, but when investigating L(G) of special forms, better results can be obtained. Wang completely analyzed the case L(G) = {3, 5}; Camach...
متن کاملCycle lengths in sparse graphs
Let C(G) denote the set of lengths of cycles in a graph G. In the first part of this paper, we study the minimum possible value of |C(G)| over all graphs G of average degree d and girth g. Erdős [7] conjectured that |C(G)| = Ω ( d ) for all such graphs, and we prove this conjecture. We also show that this is a lower bound for the number of odd cycle lengths in a graph of chromatic number d and ...
متن کاملGraphs without repeated cycle lengths
In 1975, P. Erdös proposed the problem of determining the maximum number f(n) of edges in a graph of n vertices in which any two cycles are of different lengths. In this paper, it is proved that f(n) ≥ n + 36t for t = 1260r + 169 (r ≥ 1) and n ≥ 540t2 + 175811 2 t + 7989 2 . Consequently, lim infn→∞ f(n)−n √ n ≥ √
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90037-g