Longer Cycles in Essentially 4-Connected Planar Graphs

10/16/2017
by   Igor Fabrici, et al.
0

A planar 3-connected graph G is called essentially 4-connected if, for every 3-separator S, at least one of the two components of G-S is an isolated vertex. Jackson and Wormald proved that the length circ(G) of a longest cycle of any essentially 4-connected planar graph G on n vertices is at least 2n+4/5 and Fabrici, Harant and Jendrol' improved this result to circ(G)≥1/2(n+4). In the present paper, we prove that an essentially 4-connected planar graph on n vertices contains a cycle of length at least 3/5(n+2) and that such a cycle can be found in time O(n^2).

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/25/2018

Even Longer Cycles in Essentially 4-Connected Planar Graphs

A planar graph is essentially 4-connected if it is 3-connected and every...
research
07/09/2019

A bijection for essentially 3-connected toroidal maps

We present a bijection for toroidal maps that are essentially 3-connecte...
research
02/18/2020

Dynamics of Cycles in Polyhedra I: The Isolation Lemma

A cycle C of a graph G is isolating if every component of G-V(C) is a si...
research
02/07/2022

Longest Cycle above Erdős-Gallai Bound

In 1959, Erdős and Gallai proved that every graph G with average vertex ...
research
05/11/2022

Components and Cycles of Random Mappings

Each connected component of a mapping {1,2,...,n}→{1,2,...,n} contains a...
research
06/15/2022

Pancyclicity in the Cartesian Product (K_9-C_9 )^n

A graph G on m vertices is pancyclic if it contains cycles of length l, ...
research
02/04/2021

All Subgraphs of a Wheel are 5-Coupled-Choosable

A wheel graph consists of a cycle along with a center vertex connected t...

Please sign up or login with your details

Forgot password? Click here to reset