Martinsson-Steiner Conjecture on Fractional Chromatic Number
Statement
Is the fractional chromatic number of every -degenerate triangle-free graph at most , with a matching lower bound, as conjectured by Martinsson and Steiner? The upper bound is confirmed constructively for graphs of girth at least , and the conjectured lower bound is established in a stronger form for every fixed girth; the original triangle-free case remains open.
Context
girth >= 5 case; the triangle-free case remains open
A sharp recent conjecture in graph coloring.
People
Attempts
No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
The model solved an optimization problem the authors formulated to determine the correct shape of the fractional clique function, checked and simplified probabilistic and algebraic estimates, helped draft some calculations, and pointed the authors to a key reference. The construction and overall strategy are the authors', who take full responsibility.
Reviews
No person has reviewed this attempt. It has not been checked at all.
Discussion of this attempt
no comments
Solve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.
Discussion
Nothing has been said about this problem yet.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.