منابع مشابه
Extremal Graph for Intersecting Odd Cycles
An extremal graph for a graph H on n vertices is a graph on n vertices with maximum number of edges that does not contain H as a subgraph. Let Tn,r be the Turán graph, which is the complete r-partite graph on n vertices with part sizes that differ by at most one. The well-known Turán Theorem states that Tn,r is the only extremal graph for complete graph Kr+1. Erdős et al. (1995) determined the ...
متن کاملA multipartite Ramsey number for odd cycles
In this paper we study multipartite Ramsey numbers for odd cycles. Our main result is the proof of a conjecture of Gyárfás, Sárközy and Schelp [12]. Precisely, let n ≥ 5 be an arbitrary positive odd integer; then in any two-coloring of the edges of the complete 5-partite graph K(n−1)/2,(n−1)/2,(n−1)/2,(n−1)/2,1 there is a monochromatic cycle of length n. keywords: cycles, Ramsey number, Regular...
متن کاملMultipartite Ramsey numbers for odd cycles
In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let n ≥ 5 be an arbitrary positive odd integer; then, in any two-coloring of the edges of the complete 5-partite graph K((n − 1)/2, (n − 1)/2, (n − 1)/2, (n − 1)/2, 1) there is a monochromatic Cn, ∗2000 Mathematics Subject Classification: 05C55, 05C38. †Research supported in part by the Nat...
متن کاملCycles 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 کاملGuessing Numbers of Odd Cycles
For a given number of colours, s, the guessing number of a graph is the base s logarithm of the size of the largest family of colourings of the vertex set of the graph such that the colour of each vertex can be determined from the colours of the vertices in its neighbourhood. An upper bound for the guessing number of the n-vertex cycle graph Cn is n/2. It is known that the guessing number equal...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8113