scholarly journals A Simpler Linear-Time Recognition of Circular-Arc Graphs

2006 ◽  
pp. 41-52 ◽  
Author(s):  
Haim Kaplan ◽  
Yahav Nussbaum
Keyword(s):  
Linear Time ◽  
Circular Arc ◽  
Circular Arc Graphs

scholarly journals Isomorphism of graph classes related to the circular-ones property

2013 ◽  
Vol Vol. 15 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Andrew R. Curtis ◽  
Min Chih Lin ◽  
Ross M. Mcconnell ◽  
Yahav Nussbaum ◽  
Francisco Juan Soulignac ◽  
...  
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Circular Arc ◽  
Graph Classes ◽  
Discrete Algorithms ◽  
International Audience ◽  
Related Graph ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs

Discrete Algorithms International audience We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. Our algorithm is similar to the isomorphism algorithm for interval graphs of Lueker and Booth, but works on PC trees, which are unrooted and have a cyclic nature, rather than with PQ trees, which are rooted. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, Γ circular-arc graphs, proper circular-arc graphs and convex-round graphs.

scholarly journals Linear-Time Recognition of Circular-Arc Graphs

Algorithmica ◽  
2003 ◽  
Vol 37 (2) ◽  
pp. 93-147 ◽  
Author(s):  
Ross M. McConnell
Keyword(s):  
Linear Time ◽  
Circular Arc ◽  
Circular Arc Graphs

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.

Linear time algorithms on circular-arc graphs

1991 ◽  
Vol 40 (3) ◽  
pp. 123-129 ◽  
Author(s):  
Wen-Lian Hsu ◽  
Kuo-Hui Tsai
Keyword(s):  
Linear Time ◽  
Circular Arc ◽  
Circular Arc Graphs ◽  
Linear Time Algorithms
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