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math.CO2016
Triangulability of Convex Graphs and Convex Skewness
Niran Abbas Ali, Gek L. Chia, Hazim Michman Trao +1
Motivated by a result of [1] which states that if F is a subgraph of a convex complete graph K_n and F contains no boundary edge of K_n and |E(F)| \leq n-3, then K_n - F admits a t…
math.CO2016
Non-Crossing Perfect Matchings and Triangle-Free Geometric Graphs
Hazim Michman Trao, Gek L. Chia, Niran Abbas Ali +1
We study extremal type problem arising from the question: What is the maximum number of edge-disjoint non-crossing perfect matchings on a set S of 2n points in the plane such that…
math.CO2016
Packing 1-Plane Hamiltonian Cycles in Complete Geometric Graphs
Hazim Michman Trao
Counting the number of Hamiltonian cycles that are contained in a geometric graph is {\bf \#P}-complete even if the graph is known to be planar \cite{lot:refer}. A relaxation for p…