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math.CO2025
A composition theory for upward planar orders
Xue Dong, Xuexing Lu, Yu Ye
An upward planar order on an acyclic directed graph is a special linear extension of the edge poset of that satisfies the nesting condition. This order was introduced to co…
math.CO2023
A new definition of upward planar order
Ting Li, Xuexing Lu
We give a more coherent definition of upward planar order.
math.CO2019
Planar order on vertex poset
Xuexing Lu
A planar order is a special linear extension of the edge poset (partially ordered set) of a processive plane graph. The definition of a planar order makes sense for any finite pose…
math.CO2016
Combinatorial characterization of upward planarity
Xuexing Lu, Yu Ye
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.