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The absence of efficient dual pairs of spanning trees in planar graphs
planar graphs cells
2015/8/26
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G* such that T and T* do not intersect. We show that it is not always possible to find T in ...
Numerical evidence against a conjecture on the cover time of planar graphs
Numerical evidence the cover times of planar graphs Statistical Mechanics
2011/7/28
Abstract: We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time $\tau(G_{N})$ of a planar graph $G_{N}$ o...
Contracting planar graphs to contractions of triangulations
planar graph dual graph contraction topological minor
2011/1/20
For every graph H, there exists a polynomial-time algorithm deciding if a planar input graph G can be contracted to H. However, the degree of the polynomial depends on the size of H. In this paper, we...
A Unified Framework for Trees, Multi-Dimensional Scaling and Planar Graphs
Unified Framework for Trees Multi-Dimensional Scaling Planar Graphs
2011/1/5
Least squares trees, multi-dimensional scaling and Neighbor Nets are all different and popular ways of visualizing multi-dimensional data. The method of flexi-Weighted Least Squares (fWLS) is a powerf...
Segment representation of a subclass of co-planar graphs
Segment representation a subclass of co-planar graphs
2010/11/11
A graph is said to be a segment graph if its vertices can be mapped to line segments in the plane such that two vertices have an edge between them if and only if their corresponding line segments int...
Drawing planar graphs of bounded degree with few slopes
planar graphs bounded degree few slopes
2010/12/1
settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists
a function f with the property that every planar graph G with maximum degree d admits a drawing
with nonc...
Edge Coloring of Triangle-Free 1-Planar Graphs.
In this paper the new coloring of planar, VEF-coloring, will be introduced. A VEF coloring of a simple planar graph G is a proper coloring of all elements, including vertices, edges and faces of G. We...
Classification of Regular Planar Graphs with Diameter two
graph regular diameter planar outer planar
2007/12/11
In the present paper, the regular planar graphs with diameter two are classified.