On the Bar Visibility Number of Complete Bipartite Graphs

Cao, Weiting; West, Douglas B.; Yang, Yan

doi:10.1137/19m1260268

Search citation statements

Order By: Relevance

Paper Sections

Select...

Theorem 2 ([3]1

Citation Types

Supporting

Mentioning

Contrasting

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Every planar graph has a 2-bar visibility representation in which every non-cut-vertex is assigned only one bar. The upper bound in Theorem 4 has been improved by Cao, West, and Yang [2] via a lengthy proof, yielding b(K m,n ) = r for all (m, n). In [3], the authors conjectured that b(G) ≤ ⌈n/6⌉ when G has n vertices; this must be restricted to n ≥ 7 due to K 5 and K 6 .…”

Section: Theorem 2 ([3]mentioning

confidence: 99%

Upper bounds for bar visibility of subgraphs and n-vertex graphs

Feng

West

Yang

2020

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

A t-bar visibility representation of a graph assigns each vertex up to t horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical channel of positive width. The least t such that G has a t-bar visibility representation is the bar visibility number of G, denoted by b(G). We show that if H is a spanning subgraph of G, then b(H) ≤ b(G) + 1. It follows that b(G) ≤ ⌈n/6⌉ + 1 when G is an n-vertex graph. This improves the upper bound obtained by Chang et al. (SIAM J. Discrete Math. 18 (2004) 462).

show abstract

Section: Theorem 2 ([3]mentioning

confidence: 99%