Regular Turán numbers of complete bipartite graphs

Tait, Michael; Timmons, Craig

doi:10.1016/j.disc.2021.112531

Cited by 5 publications

(3 citation statements)

References 31 publications

(46 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A number of relevant works have appeared following the public posting of our manuscript. Besides the works of Chase [6] and Chakraborti and Chen [5] already mentioned, we point out that Tait and Timmons [24] have already made the first effort at investigating the regular Turán numbers for bipartite graphs.…”

mentioning

confidence: 78%

Regular Turán numbers and some Gan–Loh–Sudakov‐type problems

Cambie

Verclos

Kang

2022

Journal of Graph Theory

View full text Add to dashboard Cite

Motivated by a Gan-Loh-Sudakov-type problem, we introduce the regular Turán numbers, a natural variation on the classical Turán numbers where we restrict ourselves to the class of regular graphs. Among other results, we prove a striking supersaturation version of Mantel's theorem in the case of a regular host graph of odd order. We also characterize the graphs for which the regular Turán numbers behave classically or otherwise.

show abstract

mentioning

confidence: 78%

Regular Turán numbers and some Gan–Loh–Sudakov‐type problems

Cambie

Verclos

Kang

2022

Journal of Graph Theory

View full text Add to dashboard Cite

show abstract

“…Another natural generalization was recently considered in [11,5,4,12,17]. Here we study rex(n, F ), which is the largest number of edges in an n-vertex regular F -free graph.…”

Section: Introductionmentioning

confidence: 99%

Generalized Rainbow Turán Numbers

Gerbner

Mészáros²,

Methuku³

et al. 2022

Electron. J. Combin.

View full text Add to dashboard Cite

Alon and Shikhelman [J. Comb. Theory, B. 121 (2016)] initiated the systematic study of the following generalized Turán problem: for fixed graphs H and F and an integer n, what is the maximum number of copies of H in an n-vertex F-free graph? An edge-colored graph is called rainbow if all its edges have different colors. The rainbow Turán number of F is defined as the maximum number of edges in a properly edge-colored graph on n vertices with no rainbow copy of F. The study of rainbow Turán problems was initiated by Keevash, Mubayi, Sudakov and Verstraete [Comb. Probab. Comput. 16 (2007)]. Motivated by the above problems, we study the following problem: What is the maximum number of copies of F in a properly edge-colored graph on n vertices without a rainbow copy of F? We establish several results, including when F is a path, cycle or tree.

show abstract

“…Recently, a variant of Turán problems have attracted attention [1,2,7,8,11], where one looks for the largest number of edges in F -free regular graphs. Here we initiate the study of regular saturation problems.…”

Section: Introductionmentioning

confidence: 99%

Saturation problems with regularity constraints

Gerbner¹,

Patkós²,

Tuza³

et al. 2020

Preprint

View full text Add to dashboard Cite

For a graph F , we say that another graph G is F -saturated, if G is F -free and adding any edge to G would create a copy of F . We study for a given graph F and integer n whether there exists a regular n-vertex F -saturated graph, and if it does, what is the smallest number of edges of such a graph. We mainly focus on the case when F is a complete graph and prove for example that there exists a K 3 -saturated regular graph on n vertices for every large enough n.We also study two relaxed versions of the problem: when we only require that no regular F -free supergraph of G should exist or when we drop the F -free condition and only require that any newly added edge should create a new copy of F .

show abstract

Regular Turán numbers of complete bipartite graphs

Cited by 5 publications

References 31 publications

Regular Turán numbers and some Gan–Loh–Sudakov‐type problems

Regular Turán numbers and some Gan–Loh–Sudakov‐type problems

Generalized Rainbow Turán Numbers

Saturation problems with regularity constraints

Contact Info

Product

Resources

About