NC algorithms for finding depth-first-search trees in interval graphs and circular-arc graphs

2002 ◽  
Author(s):  
Y. Liang ◽  
C. Rhee ◽  
S.K. Dhall ◽  
S. Lakshmivarahan
Keyword(s):  
Interval Graphs ◽  
Search Trees ◽  
Circular Arc ◽  
Depth First Search ◽  
Circular Arc Graphs ◽  
Depth First Search Trees ◽  
Nc Algorithms

Efficient algorithms for interval graphs and circular-arc graphs

Networks ◽  
1982 ◽  
Vol 12 (4) ◽  
pp. 459-467 ◽  
Author(s):  
U. I. Gupta ◽  
D. T. Lee ◽  
J. Y.-T. Leung
Keyword(s):  
Efficient Algorithms ◽  
Interval Graphs ◽  
Circular Arc ◽  
Circular Arc Graphs

On the existence of special depth first search trees

1995 ◽  
Vol 19 (4) ◽  
pp. 535-547 ◽  
Author(s):  
Ephraim Korach ◽  
Zvi Ostfeld
Keyword(s):  
Search Trees ◽  
Depth First Search ◽  
Depth First Search Trees

An Introduction to Intersection Graphs

2020 ◽  
pp. 24-65 ◽  
Author(s):  
Madhumangal Pal
Keyword(s):  
Interval Graphs ◽  
Chordal Graphs ◽  
Intersection Graph ◽  
Important Class ◽  
Intersection Graphs ◽  
Permutation Graphs ◽  
Circular Arc ◽  
String Graphs ◽  
Circular Arc Graphs ◽  
Trapezoid Graphs

In this chapter, a very important class of graphs called intersection graph is introduced. Based on the geometrical representation, many different types of intersection graphs can be defined with interesting properties. Some of them—interval graphs, circular-arc graphs, permutation graphs, trapezoid graphs, chordal graphs, line graphs, disk graphs, string graphs—are presented here. A brief introduction of each of these intersection graphs along with some basic properties and algorithmic status are investigated.

scholarly journals On Total and Edge-colouring of Proper Circular-arc Graphs

2018 ◽  
Author(s):  
João Pedro W. Bernardi ◽  
Sheila M. De Almeida ◽  
Leandro M. Zatesko
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Interval Graphs ◽  
Circular Arc ◽  
Complete Problem ◽  
Polynomial Time Algorithms ◽  
Np Complete ◽  
Polynomially Solvable ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs

Deciding if a graph is Δ-edge-colourable (resp. (Δ + 1)-total colourable), although it is an NP-complete problem for graphs in general, is polynomially solvable for interval graphs of odd (resp. even) maximum degree Δ. An interesting superclass of the proper interval graphs are the proper circular-arc graphs, for which we suspect that Δ-edge-colourability is linear-time decidable. This work presents sufficient conditions for Δ-edge-colourability, (Δ + 1)-total colourability, and (Δ+2)-total colourability of proper circular-arc graphs. Our proofs are constructive and yield polynomial-time algorithms.

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