scholarly journals Spanning cycles in regular matroids without small cocircuits

2012 ◽  
Vol 33 (8) ◽  
pp. 1765-1776 ◽  
Author(s):  
Ping Li ◽  
Hong-Jian Lai ◽  
Yehong Shao ◽  
Mingquan Zhan
Keyword(s):  
Spanning Cycles

scholarly journals Geometric Spanning Cycles in Bichromatic Point Sets

2015 ◽  
Vol 31 (2) ◽  
pp. 453-465 ◽  
Author(s):  
B. Joeris ◽  
I. Urrutia ◽  
J. Urrutia
Keyword(s):  
Point Sets ◽  
Spanning Cycles

scholarly journals On spanning cycles, paths and trees

2013 ◽  
Vol 161 (13-14) ◽  
pp. 2217-2222 ◽  
Author(s):  
Simon Mukwembi
Keyword(s):  
Spanning Cycles

scholarly journals Spanning cycles of nearly cubic graphs

1980 ◽  
Vol 29 (3) ◽  
pp. 303-309 ◽  
Author(s):  
R.C Entringer ◽  
Henda Swart
Keyword(s):  
Cubic Graphs ◽  
Spanning Cycles

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 ($O(164.17^n)$).

scholarly journals Spanning cycles in regular matroids without M∗(K5) minors

2008 ◽  
Vol 29 (1) ◽  
pp. 298-310 ◽  
Author(s):  
Hong-Jian Lai ◽  
Bolian Liu ◽  
Yan Liu ◽  
Yehong Shao
Keyword(s):  
Spanning Cycles

scholarly journals Local Resilience for Squares of Almost Spanning Cycles in Sparse Random Graphs

10.37236/6281 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Andreas Noever ◽  
Angelika Steger
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Hamiltonian Cycle ◽  
Blow Up ◽  
Minimum Degree ◽  
Single Vertex ◽  
Long Cycle ◽  
Local Resilience ◽  
Delta G ◽  
Spanning Cycles

In 1962, Pósa conjectured that a graph $G=(V, E)$ contains a square of a Hamiltonian cycle if $\delta(G)\ge 2n/3$. Only more than thirty years later Komlós, Sárkőzy, and Szemerédi proved this conjecture using the so-called Blow-Up Lemma. Here we extend their result to a random graph setting. We show that for every $\epsilon > 0$ and $p=n^{-1/2+\epsilon}$ a.a.s. every subgraph of $G_{n,p}$ with minimum degree at least $(2/3+\epsilon)np$ contains the square of a cycle on $(1-o(1))n$ vertices. This is almost best possible in three ways: (1) for $p\ll n^{-1/2}$ the random graph will not contain any square of a long cycle (2) one cannot hope for a resilience version for the square of a spanning cycle (as deleting all edges in the neighborhood of single vertex destroys this property) and (3) for $c<2/3$ a.a.s. $G_{n,p}$ contains a subgraph with minimum degree at least $cnp$ which does not contain the square of a path on $(1/3+c)n$ vertices.

Spanning Cycles in Hypercubes: 10892

2003 ◽  
Vol 110 (5) ◽  
pp. 440 ◽  
Author(s):  
Stephen C. Locke ◽  
Richard Stong
Keyword(s):  
Spanning Cycles

Spanning Cycles Through Specified Edges in Bipartite Graphs

2011 ◽  
Vol 71 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Reza Zamani ◽  
Douglas B. West
Keyword(s):  
Bipartite Graphs ◽  
Spanning Cycles
Sign in / Sign up

Export Citation Format

Share Document