A Nearly Optimal Parallel Algorithm for Constructing Depth First Spanning Trees in Planar Graphs

1988 ◽  
Vol 17 (3) ◽  
pp. 486-491 ◽  
Author(s):  
Xin He ◽  
Yaacov Yesha
Keyword(s):  
Parallel Algorithm ◽  
Planar Graphs ◽  
Spanning Trees

scholarly journals Minimum congestion spanning trees in planar graphs

2010 ◽  
Vol 310 (6-7) ◽  
pp. 1204-1209 ◽  
Author(s):  
M.I. Ostrovskii
Keyword(s):  
Planar Graphs ◽  
Spanning Trees

scholarly journals Counting Triangulations of Planar Point Sets

10.37236/557 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Micha Sharir ◽  
Adam Sheffer
Keyword(s):  
Upper Bound ◽  
Planar Graphs ◽  
Spanning Trees ◽  
Upper Bounds ◽  
Line Graphs ◽  
Point Sets ◽  
Planar Point ◽  
Straight Line ◽  
Point Set ◽  
Spanning Cycles

We study the maximal number of triangulations that a planar set of $n$ points can have, and show that it is at most $30^n$. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of $43^n$ for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set. Specifically, it can be used to derive new upper bounds for the number of planar graphs ($207.84^n$), spanning cycles ($O(68.67^n)$), spanning trees ($O(146.69^n)$), and cycle-free graphs ($O(164.17^n)$).

A parallel algorithm for the enumeration of the spanning trees of a graph

1984 ◽  
Vol 1 (3-4) ◽  
pp. 275-286 ◽  
Author(s):  
Shao-Wen Mai ◽  
D.J. Evans
Keyword(s):  
Parallel Algorithm ◽  
Spanning Trees

scholarly journals Rotor-Routing and Spanning Trees on Planar Graphs

2014 ◽  
Vol 2015 (11) ◽  
pp. 3225-3244 ◽  
Author(s):  
Melody Chan ◽  
Thomas Church ◽  
Joshua A. Grochow
Keyword(s):  
Planar Graphs ◽  
Spanning Trees
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