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Graph Theory and Combinatorics Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Gregory 307
Date
Feb 13, 2024   1:00 pm  
Speaker
Peter Bradshaw (UIUC)
Contact
Peter Bradshaw
E-Mail
pb38@illinois.edu
Views
13
Originating Calendar
Combinatorics Research Area Calendar

Speaker: Peter Bradshaw (UIUC)

Title: List-avoiding orientations

Given a graph G with a set F(v) of forbidden values at each vertex v, an F-avoiding orientation of G is an orientation in which the out-degree at v is not in F(v) for each vertex v. Akbari, Dalirrooyfard, Ehsani, Ozeki, and Sherkati conjectured that if |F(v)| < deg(v)/2 for each v, then G has an F-avoiding orientation, and they showed that this statement is true when the upper bound is replaced by deg(v)/4. In this paper, we take a step toward this conjecture by proving that if |F(v)| < deg(v)/3 for each vertex v, then G has an F-avoiding orientation. Furthermore, we show that if the maximum degree of G is subexponential in terms of the minimum degree, then this coefficient of 1/3 can be increased to 0.414. Our main tool is a new sufficient condition for the existence of an F-avoiding orientation based on the Combinatorial Nullstellensatz of Alon and Tarsi.

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