Book Chapter10.1007/3-540-17218-1_57
Recognizing Outerplanar Graphs in Linear Time
Manfred Wiegers
- 17 Jun 1986
- pp 165-176
43
TL;DR: A linear time algorithm to determine whether an arbitrary graph is outerplanar is described, which works without splitting the graph into its biconnected components or using bucket sort to give the adjacency lists a special order.
read more
Abstract: This paper describes a linear time algorithm to determine whether an arbitrary graph is outerplanar. The algorithm uses an edge coloring technique and deletes successively vertices of degree less than or equal to two. If the degree of a vertex is two, both neighbors of the vertex are joined by an edge. The algorithm works without splitting the graph into its biconnected components or using bucket sort to give the adjacency lists a special order.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The Steiner Forest Problem revisited
TL;DR: It is partially answered by showing that SFP is strongly NP-hard on graphs with treewidth 3, and a quadratic time algorithm for the special case on outerplanar graphs is suggested.
33
The Lexicographically First Maximal Subgraph Problems: P-Completeness and NC Algorithms
Satoru Miyano,Satoru Miyano +1 more
- 13 Jul 1987
TL;DR: The main contribution of this paper is theP-completeness of the lfm subgraph problem for any nontrivial hereditary property and it is shown that the lfmedge-induced sub graph problem for some graph properties and show that it has a different complexity feature.
32
•Dissertation
On index coding with side information
Son Hoang Dau
- 01 Jan 2012
TL;DR: The block security level of the linear index code based on a linear version of the ICSI code is analyzed to fill in the gap in the security and error correction aspects of those codes.
27
Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs
TL;DR: This work presents space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using O(n+min{m,nloglogn}) bits and shows an algorithm for the recognition of (maximal) outerplanar graphs in O( n) bits.
References
Efficient Planarity Testing
TL;DR: An efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane is described, which used depth-first search and has time and space bounds.
Linear algorithms to recognize outerplanar and maximal outerplanar graphs
TL;DR: We present conceptually simpler algorithms to determine if a graph is a maximalouterplanar or outerplanar graph, based on the fact that the graph has a unique Hamiltonian cycle.