Norishige Chiba

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

A linear 5-coloring algorithm of planar graphs

a(G)

A linear algorithm for five-coloring a planar graph

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

An algorithm for finding a large independent set in planar graphs

O(a(G)m)

Planar Graphs: Theory and Algorithms

time. Since

Linear algorithms for convex drawings of planar graphs

a(G)

A theorem on paths in planar 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

Planar graphs: theory and applications

K_l