34 citations · 84 across the 36 of their papers we have counts for
6 papers · 1 filter
On Convex Graphs Having Plane Spanning Subgraph of Certain Type
Niran Abbas Ali, Gek L. Chiab, Hazim Michman Traoc +1
Motivated by a result of [17], we determine necessary and sufficient conditions on $F\/$ with $|E(F)| \leq n-1\/$ for which $K_n - F\/$ admits a -angulation. For $|E(F)| \geq n\…
On Edge-Partitioning of Complete Geometric Graphs into Plane Trees
Hazim Michman Trao, Gek L. Chia, Niran Abbas Ali +1
In response to a well-known open question ``Does every complete geometric graph on $2n\/$ vertices have a partition of its edge set into $n\/$ plane spanning trees?" we provide an…
On the maximum number of edges in plane graph with fixed exterior face degree
Niran Abbas Ali, Gek L. Chiab, Hazim Michman Trao +1
A well known Euler's formula consequence's corollary in graph theory states that: For a connected simple planar graph with vertices and edges, and girth , we have $m \le…
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…
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…
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…