Stack and Queue Layouts of Directed Acyclic Graphs: Part I
SIAM Journal on Computing
Stack and Queue Layouts of Directed Acyclic Graphs: Part II
SIAM Journal on Computing
A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Level Planarity Testing in Linear Time
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
Characterization of unlabeled level planar trees
Computational Geometry: Theory and Applications
Minimum level nonplanar patterns for trees
GD'07 Proceedings of the 15th international conference on Graph drawing
Layer-free upward crossing minimization
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Hanani-Tutte and monotone drawings
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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We consider characterizations of level planar trees. Healy et al. [8] characterized the set of trees that are level planar in terms of two minimal level non-planar (MLNP) patterns. Fowler and Kobourov [7] later proved that the set of patterns was incomplete and added two additional patterns. In this paper, we show that the characterization is still incomplete by providing new MLNP patterns not included in the previous characterizations. Moreover, we introduce an iterative method to create an arbitrary number of MLNP patterns, thus proving that the set of minimal patterns that characterizes level planar trees is infinite.