Benjamin Iriarte

Graph Orientations and Linear Extensions.
dmtcs:2455 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2014,
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)

https://doi.org/10.46298/dmtcs.2455
Graph Orientations and Linear Extensions.
Authors: Benjamin Iriarte ^{1}
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Benjamin Iriarte
1 Department of Mathematics [MIT]
Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph, and therefore we can count the number of linear extensions of these posets. We want to know which choice of orientation maximizes the number of linear extensions of the corresponding poset, and this problem is solved essentially for comparability graphs and odd cycles, presenting several proofs. We then provide an inequality for general graphs and discuss further techniques.
Conte, Alessio; Grossi, Roberto; Marino, Andrea; Rizzi, Romeo, 2016, Listing Acyclic Orientations Of Graphs With Single And Multiple Sources, LATIN 2016: Theoretical Informatics, pp. 319333, 10.1007/9783662495292_24.