Polynomial time recognition of unit circular-arc graphs

2006 ◽  
Vol 58 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Guillermo Durán ◽  
Agustín Gravano ◽  
Ross M. McConnell ◽  
Jeremy Spinrad ◽  
Alan Tucker
Keyword(s):  
Polynomial Time ◽  
Circular Arc ◽  
Circular Arc Graphs

scholarly journals Novel Procedures for Graph Edge-colouring

2019 ◽  
Author(s):  
Leandro M. Zatesko ◽  
Renato Carmo ◽  
André L. P. Guedes
Keyword(s):  
Uniform Distribution ◽  
Polynomial Time ◽  
Chordal Graphs ◽  
Circular Arc ◽  
Simple Graphs ◽  
Degree Sum ◽  
Local Degree ◽  
Polynomial Time Algorithms ◽  
Circular Arc Graphs ◽  
Edge Colouring

We present a novel recolouring procedure for graph edge-colouring. We show that all graphs whose vertices have local degree sum not too large can be optimally edge-coloured in polynomial time. We also show that the set ofthe graphs satisfying this condition includes almost every graph (under the uniform distribution). We present further results on edge-colouring join graphs, chordal graphs, circular-arc graphs, and complementary prisms, whose proofs yield polynomial-time algorithms. Our results contribute towards settling the Over- full Conjecture, the main open conjecture on edge-colouring simple graphs. Fi- nally, we also present some results on total colouring.

Surjective L (2, 1)-labeling of cycles and circular-arc graphs

2018 ◽  
Vol 35 (1) ◽  
pp. 739-748 ◽  
Author(s):  
Sk. Amanathulla ◽  
Madhumangal Pal
Keyword(s):  
Circular Arc ◽  
Circular Arc Graphs

An $O(n^2 )$ Algorithm for Coloring Proper Circular Arc Graphs

1981 ◽  
Vol 2 (2) ◽  
pp. 88-93 ◽  
Author(s):  
James B. Orlin ◽  
Maurizio A. Bonuccelli ◽  
Daniel P. Bovet
Keyword(s):  
Circular Arc ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs

scholarly journals Structural results on circular-arc graphs and circle graphs: A survey and the main open problems

2014 ◽  
Vol 164 ◽  
pp. 427-443 ◽  
Author(s):  
Guillermo Durán ◽  
Luciano N. Grippo ◽  
Martín D. Safe
Keyword(s):  
Open Problems ◽  
Circle Graphs ◽  
Circular Arc ◽  
Circular Arc Graphs
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