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Title:Cover-incomparability graphs and chordal graphs
Authors:ID Brešar, Boštjan (Author)
ID Changat, Manoj (Author)
ID Dravec, Tanja (Author)
ID Mathews, Joseph (Author)
ID Mathews, Antony (Author)
Files:URL http://dx.doi.org/10.1016/j.dam.2010.07.001
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Problem prepoznavanja grafov pokritij-neprimerljivosti (to je grafov, ki jih dobimo iz delno urejenih množic kot povezavno unijo njihovega grafa pokritij in grafa neprimerljivosti) je NP-poln v splošnem, kot so dokazali v [J. Maxová, P. Pavlíkova, A. Turzík, On the complexity of cover-incomparability graphs of posets, Order 26 (2009) 229-236], medtem ko je na primer očitno polinomski v razredu dreves. V tem članku se osredotočimo na razrede tetivnih grafov in dokažemo, da je vsak graf pokritij-neprimerljivosti, ki je tetiven graf, kar graf intervalov. Okarakteriziramo tiste delno urejene množice, ki imajo za graf pokritij-neprimerljivosti bločni graf, oziroma razcepljeni graf in tudi okarakteriziramo grafe pokritij-neprimerljivosti med bločnimi, oziroma razcepljenimi grafi. Slednji karakterizaciji dasta tudi linearen algoritem za prepoznavanje bločnih, oziroma razcepljenih grafov, ki so grafi pokritij-neprimerljivosti.
Keywords:matematika, teorija grafov, delno urejena množica, temeljni graf, tetiven graf, razcepljen graf, bločni graf, mathematics, graph theory, poset, underlying graph, chordal graph, split graf, block graph
Year of publishing:2010
Number of pages:str. 1752-1759
Numbering:Vol. 158, iss. 16
PID:20.500.12556/DKUM-51869 New window
UDC:519.17
ISSN on article:0166-218X
COBISS.SI-ID:15656537 New window
NUK URN:URN:SI:UM:DK:ETFEWXAE
Publication date in DKUM:10.07.2015
Views:1471
Downloads:94
Metadata:XML DC-XML DC-RDF
Categories:Misc.
:
BREŠAR, Boštjan, CHANGAT, Manoj, DRAVEC, Tanja, MATHEWS, Joseph and MATHEWS, Antony, 2010, Cover-incomparability graphs and chordal graphs. Discrete applied mathematics [online]. 2010. Vol. 158, no. 16, p. 1752–1759. [Accessed 28 March 2025]. Retrieved from: http://dx.doi.org/10.1016/j.dam.2010.07.001
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Record is a part of a journal

Title:Discrete applied mathematics
Shortened title:Discrete appl. math.
Publisher:Elsevier
ISSN:0166-218X
COBISS.SI-ID:25342464 New window

Secondary language

Language:Unknown
Title:Grafi pokritij-neprimerljivosti in tetivni grafi
Abstract:The problem of recognizing cover-incomparability graphs (i.e. the graphs obtained from posets as the edge-union of their covering and incomparability graph) was shown to be NP-complete in general [J. Maxová, P. Pavlíkova, A. Turzík, On the complexity of cover-incomparability graphs of posets, Order 26 (2009) 229-236], while it is for instance clearly polynomial within trees. In this paper we concentrate on (classes of) chordal graphs, and show that any cover-incomparability graph that is a chordal graph is an interval graph. We characterize the posets whose cover-incomparability graph is a block graph, and a split graph, respectively, and also characterize the cover-incomparability graphs among block and split graphs, respectively. The latter characterizations yield linear time algorithms for the recognition of block and split graphs, respectively, that are cover-incomparability graphs.


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