Polynomial time algorithms on circular-arc overlap graphs

Networks ◽  
1991 ◽  
Vol 21 (2) ◽  
pp. 195-203 ◽  
Author(s):  
Toshinobu Kashiwabara ◽  
Sumio Masuda ◽  
Kazuo Nakajima ◽  
Toshio Fujisawa
Keyword(s):  
Polynomial Time ◽  
Circular Arc ◽  
Polynomial Time Algorithms ◽  
Overlap 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.

ALGORITHMS ON SUBGRAPH OVERLAP GRAPHS

2014 ◽  
Vol 06 (02) ◽  
pp. 1450018 ◽  
Author(s):  
FANICA GAVRIL
Keyword(s):  
Polynomial Time ◽  
Intersection Graph ◽  
Maximum Weight ◽  
Intersection Graphs ◽  
Polynomial Time Algorithms ◽  
The Family ◽  
Overlap Graphs ◽  
Hereditary Properties

Consider a graph D and a family FI of connected edge subgraphs of D. Let GI(V, F) be the intersection graph of FI and G the overlap graph of FI. We describe polynomial time algorithms for subgraph overlap graphs G when their intersection graphs GI have specific hereditary properties. The algorithms are to find maximum induced complete bipartite subgraphs, maximum weight holes of a given parity, minimum dominating holes, antiholes of a given parity and some others. In addition, we define the family of subgraph filament graphs based on D, FI and GI, and prove it to be the same as the family of subgraph overlap graphs.

scholarly journals An Overview of Algorithms for Network Survivability

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
F. A. Kuipers
Keyword(s):  
Polynomial Time ◽  
Network Connectivity ◽  
Network Survivability ◽  
Disjoint Paths ◽  
Polynomial Time Algorithms ◽  
Concise Overview ◽  
Main Components

Network survivability—the ability to maintain operation when one or a few network components fail—is indispensable for present-day networks. In this paper, we characterize three main components in establishing network survivability for an existing network, namely, (1) determining network connectivity, (2) augmenting the network, and (3) finding disjoint paths. We present a concise overview of network survivability algorithms, where we focus on presenting a few polynomial-time algorithms that could be implemented by practitioners and give references to more involved algorithms.

scholarly journals Reconstruction of score sets

2014 ◽  
Vol 6 (2) ◽  
pp. 210-229
Author(s):  
Antal Iványi
Keyword(s):  
Polynomial Time ◽  
Constructive Proof ◽  
Construction Algorithm ◽  
Polynomial Time Algorithms ◽  
General Polynomial ◽  
Degree Set ◽  
New Algorithms

Abstract The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.

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