New exact values of the maximum size of graphs free of topological complete subgraphs

Balbuena, C.; Cera, M.; Diánez, A.; García–Vázquez, P.

doi:10.1016/j.disc.2006.07.031

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[4]) devoted to this subject and the contributions on this topic (cf. [5,9,14,19,20,22])). The second was stated by Zarankiewicz (cf.…”

Section: Introductionmentioning

confidence: 99%

Topological minors in bipartite graphs

Balbuena

Cera

García–Vázquez

et al. 2011

Acta. Math. Sin.-English Ser.

View full text Add to dashboard Cite

For a bipartite graph G on m and n vertices, respectively, in its vertices classes, and for integers s and t such that 2 ≤ s ≤ t, 0 ≤ m − s ≤ n − t, and m + n ≤ 2s + t − 1, we prove that if G has at least mn − (2(m − s) + n − t) edges then it contains a subdivision of the complete bipartite K (s,t) with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn − (2(m − s) + n − t + 1) edges for this topological Turan type problem.

show abstract

“…[4]) devoted to this subject and the contributions on this topic (cf. [5,9,14,19,20,22])). The second was stated by Zarankiewicz (cf.…”

Section: Introductionmentioning

confidence: 99%