The Sub-Exponential Transition for the Chromatic Generalized Ramsey Numbers

Lee, Choongbum; Tran, Brandon

doi:10.1007/s00493-017-3474-6

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [21], Fox, Pach and Suk studied the semi-algebraic variant of the Erdős-Gyárfás function. A chromatic number version of the Erdős-Gyárfás function was considered in [9,28]. For more information on this topic, we refer the interested reader to [11,Section 3.5.1] and [32,Section 7].…”

Section: Introductionmentioning

confidence: 99%

Growth rates of the bipartite Erdős-Gyárfás function

Li¹,

Broersma

Wang³

2021

Preprint

View full text Add to dashboard Cite

Given two graphs G, H and a positive integer q, an (H, q)-coloring of G is an edge-coloring of G such that every copy of H in G receives at least q distinct colors. The bipartite Erdős-Gyárfás function r(K n,n , K s,t , q) is defined to be the minimum number of colors needed for K n,n to have a (K s,t , q)-coloring. For balanced complete bipartite graphs K p,p , the function r(K n,n , K p,p , q) was studied systematically in [Axenovich, Füredi and Mubayi, J. Combin. Theory Ser. B 79 (2000), 66-86]. In this paper, we study the asymptotic behavior of this function for complete bipartite graphs K s,t that are not necessarily balanced. Our main results deal with thresholds and lower and upper bounds for the growth rate of this function, in particular for (sub)linear and (sub)quadratic growth. We also obtain new lower bounds for the balanced bipartite case, and improve several results given by Axenovich, Füredi and Mubayi. Our proof techniques are based on an extension to bipartite graphs of the recently developed Color Energy Method by Pohoata and Sheffer and its refinements, and a generalization of an old result due to Corrádi.

show abstract

Section: Introductionmentioning

confidence: 99%

Growth rates of the bipartite Erdős-Gyárfás function

Li¹,

Broersma

Wang³

2021

Preprint

View full text Add to dashboard Cite

show abstract

Growth rates of the bipartite Erdős–Gyárfás function

Li,

Broersma,

Wang

2024

Journal of Graph Theory

View full text Add to dashboard Cite

Given two graphs and a positive integer , an ‐coloring of is an edge‐coloring of such that every copy of in receives at least distinct colors. The bipartite Erdős–Gyárfás function is defined to be the minimum number of colors needed for to have a ‐coloring. For balanced complete bipartite graphs , the function was studied systematically in Axenovich et al. In this paper, we study the asymptotic behavior of this function for complete bipartite graphs that are not necessarily balanced. Our main results deal with thresholds and lower and upper bounds for the growth rate of this function, in particular for (sub)linear and (sub)quadratic growth. We also obtain new lower bounds for the balanced bipartite case, and improve several results given by Axenovich, Füredi and Mubayi. Our proof techniques are based on an extension to bipartite graphs of the recently developed Color Energy Method by Pohoata and Sheffer and its refinements, and a generalization of an old result due to Corrádi.

show abstract

The Sub-Exponential Transition for the Chromatic Generalized Ramsey Numbers

Cited by 2 publications

References 8 publications

Growth rates of the bipartite Erdős-Gyárfás function

Growth rates of the bipartite Erdős-Gyárfás function

Growth rates of the bipartite Erdős–Gyárfás function

Contact Info

Product

Resources

About