scholarly journals Edge-Disjoint Paths in Planar Graphs

2004 ◽  
Author(s):  
C. Chekuri ◽  
S. Khanna ◽  
F.B. Shepherd
Keyword(s):  
Planar Graphs ◽  
Disjoint Paths ◽  
Edge Disjoint

scholarly journals Edge-Disjoint Paths in Planar Graphs with Constant Congestion

2009 ◽  
Vol 39 (1) ◽  
pp. 281-301 ◽  
Author(s):  
Chandra Chekuri ◽  
Sanjeev Khanna ◽  
F. Bruce Shepherd
Keyword(s):  
Planar Graphs ◽  
Disjoint Paths ◽  
Edge Disjoint

scholarly journals On the Maximum Degree of Path-Pairable Planar Graphs

10.37236/7291 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
António Girão ◽  
Gábor Mészáros ◽  
Kamil Popielarz ◽  
Richard Snyder
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Disjoint Paths ◽  
Edge Disjoint ◽  
Finite Genus

A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in path-pairable planar graphs. We show that any $n$-vertex path-pairable planar graph must contain a vertex of degree linear in $n$. Our result generalizes to graphs embeddable on a surface of finite genus.  

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