Takao Nishizeki

Arboricity and subgraph listing algorithms

In this paper we introduce a new simple strategy into edge-searching of a graph, which is useful to the various subgraph listing problems. Applying the strategy, we obtain the following four algorithms. The first one lists all the triangles in a graph G in

A linear algorithm for embedding planar graphs using PQ -trees

O(a(G)m)

Drawing Plane Graphs Nicely

time, where m is the number of edges of G and

Multiple assignment scheme for sharing secret

a(G)

The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs

the arboricity of G. The second finds all the quadrangles in

On the 1.1 edge-coloring of multigraphs

O(a(G)m)

Algorithms for routing around a rectangle

time. Since

The edge-disjoint path problem is NP-complete for series-parallel graphs

a(G)

Grid Drawings of 4-Connected Plane Graphs

is at most three for a planar graph G, both run in linear time for a planar graph. The third lists all the complete subgraphs

Rectangular grid drawings of plane graphs

K_l