A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs

1982 ◽  
Vol 6 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Dale J. Skrien
Keyword(s):  
Interval Graphs ◽  
Circular Arc ◽  
Triangulated Graphs ◽  
Circular Arc Graphs ◽  
Proper 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.

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 The Chromatic Index of Proper Circular-arc Graphs of Odd Maximum Degree which are Chordal

2019 ◽  
Vol 346 ◽  
pp. 125-133
Author(s):  
João Pedro W. Bernardi ◽  
Murilo V.G. da Silva ◽  
André Luiz P. Guedes ◽  
Leandro M. Zatesko
Keyword(s):  
Maximum Degree ◽  
Chromatic Index ◽  
Circular Arc ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs

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

scholarly journals On chordal proper circular arc graphs

1994 ◽  
Vol 128 (1-3) ◽  
pp. 395-398 ◽  
Author(s):  
Jørgen Bang-Jensen ◽  
Pavol Hell
Keyword(s):  
Circular Arc ◽  
Circular Arc Graphs ◽  
Proper Circular Arc Graphs
Sign in / Sign up

Export Citation Format

Share Document