Cuts in matchings of 3-edge-connected cubic graphs

12/17/2017
by   Kolja Knauer, et al.
0

We discuss relations between several known (some false, some open) conjectures on 3-edge-connected, cubic graphs and how they all fit into the same framework related to cuts in matchings. We then provide a construction of 3-edge-connected digraphs satisfying the property that for every even subgraph E, the graph obtained by contracting the edges of E is not strongly connected. This disproves a recent conjecture of Hochstättler [A flow theory for the dichromatic number. European Journal of Combinatorics, 66, 160--167, 2017]. Furthermore, we show that an open conjecture of Neumann-Lara holds for all planar graphs on at most 26 vertices.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/03/2023

Frank number and nowhere-zero flows on graphs

An edge e of a graph G is called deletable for some orientation o if the...
research
10/24/2019

A Note on Colourings of Connected 2-edge Coloured Cubic Graphs

In this short note we show that every connected 2-edge coloured cubic gr...
research
08/17/2020

Sublinear bounds for nullity of flows and approximating Tutte's flow conjectures

A function f:N→ N is sublinear, if lim_x→ +∞f(x)/x=0. If A is ...
research
02/23/2022

Matching Theory and Barnette's Conjecture

Barnette's Conjecture claims that all cubic, 3-connected, planar, bipart...
research
12/21/2017

Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44

The family of snarks -- connected bridgeless cubic graphs that cannot be...
research
09/04/2019

On a Conjecture of Lovász on Circle-Representations of Simple 4-Regular Planar Graphs

Lovász conjectured that every connected 4-regular planar graph G admits ...
research
06/29/2018

Generating Connected Random Graphs

We present an algorithm to produce connected random graphs using a Metro...

Please sign up or login with your details

Forgot password? Click here to reset