Drawing Halin-graphs with small height

Drawing Planar Graphs with Reduced Height

A straight-line (respectively, polyline) drawing Γ of a planar graph G on a set Lk of k parallel lines is a planar drawing that maps each vertex of G to a distinct point on Lk and each edge of G to a straight line segment (respectively, a polygonal chain with the bends on Lk) between its endpoints. The height of Γ is k, i.e., the number of lines used in the drawing. In this paper we compute new...

Drawing High-degree Graphs with Small Grid-size Drawing High-degree Graphs with Small Grid-size

In this paper, we present a general scheme to produce interactive and static orthogonal drawings of graphs. As opposed to most known algorithms, we do not restrict ourselves to graph with maximum degree 4, but allow arbitrary degrees. We show here how, with one speciic implementation of the scheme, we can obtain an m+n 2 m+n 2-grid for all simple connected graphs without nodes of degree 1. Furt...

Drawing planar bipartite graphs with small area

Boxicity of Halin graphs

A k-dimensional box is the Cartesian product R1 × R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such ...

Dominating cycles in halin graphs

A cycle in a graph is dominating if every vertex lies at distance at most one from the cycle and a cycle is D-cycle if every edge is incident with a vertex of the cycle. In this paper, first we provide recursive formulae for finding a shortest dominating cycle in a Hahn graph; minor modifications can give formulae for finding a shortest D-cycle. Then, dominating cycles and D-cycles in a Halin g...