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On claw-free asteroidal triple-free graphs

2002
*
Discrete Applied Mathematics
*

We present an O(n 2:376 ) algorithm for recognizing

doi:10.1016/s0166-218x(01)00208-6
fatcat:7isrygxg3ndvnpa6t5ud22bx6u
*claw*-*free*AT-*free**graphs*and a linear-time algorithm for computing the set of all central vertices of a*claw*-*free*AT-*free**graph*. ... Our algorithms exploit the structure of 2LexBFS schemes of*claw*-*free*AT-*free**graphs*. ? ... A*graph*G is called*asteroidal**triple*-*free*(AT-*free*) if it has no*asteroidal**triple*. An AT-*free**graph*is*claw*-*free*AT-*free*if it does not contain a*claw*as an induced subgraph. ...##
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On Claw-Free Asteroidal Triple-Free Graphs
[chapter]

1999
*
Lecture Notes in Computer Science
*

We present an O(n 2:376 ) algorithm for recognizing

doi:10.1007/3-540-46784-x_35
fatcat:4ix47kqhenekjaqv7fsvqnihvm
*claw*-*free*AT-*free**graphs*and a linear-time algorithm for computing the set of all central vertices of a*claw*-*free*AT-*free**graph*. ... Our algorithms exploit the structure of 2LexBFS schemes of*claw*-*free*AT-*free**graphs*. ? ... A*graph*G is called*asteroidal**triple*-*free*(AT-*free*) if it has no*asteroidal**triple*. An AT-*free**graph*is*claw*-*free*AT-*free*if it does not contain a*claw*as an induced subgraph. ...##
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Algorithms for the Recognition of Net-free Graphs and for Computing Maximum Cardinality Matchings in Claw-free Graphs

2014
*
Studies in Informatics and Control
*

During the last decades, numerous studies have been undertaken

doi:10.24846/v23i2y201406
fatcat:rv6tfr2t2fbpzgzr4vwkr4xm4m
*on*the classes of net-*free**graphs*,*claw*-*free**graphs*, and the relationship between them. ... In this article, we give a characterization of net-*free**graphs*, a characterization of*claw*-*free**graphs*, using weakly decomposition. ... STEWART,*Asteroidal**Triple*-*free**Graphs*, SIAM J. Discrete Math., vol. 10, 1997, pp. 399-430. ...##
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Approximating the bandwidth for asteroidal triple-free graphs
[chapter]

1995
*
Lecture Notes in Computer Science
*

Then (G) 2 implies that G is

doi:10.1007/3-540-60313-1_161
fatcat:fe3ku6hczfhyvalakh42gx4bzy
*claw*-*free*. Hence G is*claw*-*free*and AT-*free*and this implies bw(G) = tw(G) by Theorem 3.12. ... when restricted to cocomparability*graphs*or to AT-*free**graphs*. ... A*graph*is*asteroidal**triple**free*(AT-*free*) if it contains no*asteroidal**triple*. Definition 3. 2 2 Let G = (V; E) and x; y 2 V. ...##
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Characterising AT-free Graphs with BFS
[article]

2018
*
arXiv
*
pre-print

An

arXiv:1807.05065v1
fatcat:ubnc6vlmuzburj5ty5yxcx5eby
*asteroidal**triple**free**graph*is a*graph*such that for every independent*triple*of vertices no path between any two avoids the third. ... Furthermore, we give a linear time algorithm which employs multiple applications of (L)BFS to compute AT-*free*orders in*claw*-*free*AT-*free**graphs*and a generalisation of these. ... As shown in [7] , a*graph*G is an*asteroidal**triple**free**graph*if and only if every connected induced subgraph of G has the spine property. ...##
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Page 4037 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

4037
edge-color a bipartite

*graph*with n nodes, m edges, and maximum degree A.” 2003f:05098 05C75 Hempel, Harald (D-FSUMI,; Jena); Kratsch, Dieter (D-FSUMI; Jena)*On**claw*-*free**asteroidal**triple*-*free**graphs*... The algorithms are based*on*structural properties of 2LexBFS schemes for*claw*-*free*AT-*free**graphs*. ...##
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Obstructions to chordal circular-arc graphs of small independence number

2013
*
Electronic Notes in Discrete Mathematics
*

This is akin to the notion of

doi:10.1016/j.endm.2013.10.012
fatcat:xkph4nvkdfenvf437g4jktrnw4
*asteroidal**triple*used in the classical characterization of interval*graphs*by Lekkerkerker and Boland [10] . ... We then focus*on*chordal*graphs*, and study the relationship between the structure of chordal*graphs*and the presence/absence of blocking quadruples. Our contribution is two-fold. ... for this paper, they characterized*claw*-*free*chordal circular-arc*graphs*. ...##
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On linear and circular structure of (claw, net)-free graphs

2003
*
Discrete Applied Mathematics
*

We show also how

doi:10.1016/s0166-218x(02)00571-1
fatcat:2pbmjgfx7zfj7hwy3cz2djmtlm
*one*can use structural properties of (*claw*, net)-*free**graphs*to solve e ciently the domination, independent domination, and independent set problems*on*these*graphs*. ? ... We prove that every (*claw*, net)-*free**graph*contains an induced doubly dominating cycle or a dominating pair. ...*one*example of an*asteroidal**triple*. ...##
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Induced matchings in asteroidal triple-free graphs

2003
*
Discrete Applied Mathematics
*

We ÿrst deÿne a wider class of

doi:10.1016/s0166-218x(03)00390-1
fatcat:gtwpwwjlqbg5ldlcml4ofzitwq
*graphs*called the line-*asteroidal**triple*-*free*(LAT-*free*)*graphs*which contains AT-*free**graphs*as a subclass. ... -separated matching problem,*on*LAT-*free**graphs*can be solved in polynomial time. ... A*graph*is called line-*asteroidal**triple*-*free*(LAT-*free*) if it does not contain a LAT. ...##
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Contents

2003
*
Discrete Applied Mathematics
*

Mosca

doi:10.1016/s0166-218x(03)00587-0
fatcat:s4xzqhrk6vaq3euwplh4zfo24y
*On*the structure and stability number of P 5 -and co-chair-*free**graphs*47 J.-M. Chang Induced matchings in*asteroidal**triple*-*free**graphs*67 R.J. Faudree, Z. Ryj ! acˇek and R.H. ... Schelp*On*local and global independence numbers of a*graph*79 O. Favaron Independence and upper irredundance in*claw*-*free**graphs*85 A. Finbow, B. Hartnell, R. Nowakowski and M.D. ...##
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AT-free graphs: linear bounds for the oriented diameter

2004
*
Discrete Applied Mathematics
*

Let G be a bridgeless connected undirected (b.c.u.)

doi:10.1016/s0166-218x(03)00376-7
fatcat:hkiddpjv45dv7jvejnnc2z7lh4
*graph*. ... A*graph*is AT-*free*if it does not contain an*asteroidal**triple*.*Asteroidal**triples*were introduced to characterize interval*graphs*[14] . ... Thus {s a(i) ; s a(i+1)−1 ; p i } is an*asteroidal**triple*. (2) It follows by symmetry from part (1). Theorem 12. Let G be an AT-*free**graph*. ...##
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Boxicity and cubicity of asteroidal triple free graphs

2010
*
Discrete Mathematics
*

A

doi:10.1016/j.disc.2010.01.020
fatcat:blgsakh46jdsrodwtnp4ugcaq4
*graph*is*asteroidal**triple**free*(AT-*free*) if it has no*asteroidal**triple*. The class of AT-*free**graphs*contains the classes of interval, permutation, trapezoid, and cocomparability*graphs*. ... Upper bound*on*boxicity of AT-*free**graphs*and cubicity of*claw*-*free*AT-*free**graphs*In this section, we obtain upper bounds*on*boxicity of AT-*free**graphs*and cubicity of*claw*-*free*AT-*free**graphs*. ...##
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Author index to volume

2003
*
Discrete Applied Mathematics
*

Mosca,

doi:10.1016/s0166-218x(03)00591-2
fatcat:vut2tfclizgvdnot7fn7dd4tou
*On*the structure and stability number of P 5 -and co-chair-*free**graphs*(1-3) 47-65 Chang, J.-M., Induced matchings in*asteroidal**triple*-, R.J., Z. Ryj! aek and R.H. ... Schelp,*On*local and global independence numbers of a*graph*(1-3) 79-84 Favaron, O., Independence and upper irredundance in*claw*-*free**graphs*(1-3) 85-95 Finbow, A., B. Hartnell, R. ...##
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Boxicity and Cubicity of Asteroidal Triple free graphs
[article]

2009
*
arXiv
*
pre-print

Let G be an AT-

arXiv:0812.0894v2
fatcat:mnrbwranvbayhl3eq652xbffqi
*free**graph*with chromatic number χ(G) and*claw*number . In this paper we will show that (G) ≤χ(G) and this bound is tight. We also show that (G) ≤(G)(_2 +2) ≤ χ(G)(_2 +2). ... If G is an AT-*free**graph*having girth at least 5 then (G) ≤ 2 and therefore (G) ≤ 2_2 +4. ... A*graph*is called*asteroidal**triple**free*(AT-*free*for short) if it does not contain an*asteroidal**triple*. ...##
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Induced matchings in intersection graphs

2004
*
Discrete Mathematics
*

In particular, we show that if G is a polygon-circle

doi:10.1016/j.disc.2003.05.001
fatcat:glgc57tm2jd4totyihmatyv3ua
*graph*, then so is [L(G)] 2 , and the same holds for*asteroidal**triple*-*free*and interval-ÿlament*graphs*. ... Gavril's interval-ÿlament*graphs*include cocomparability and polygon-circle*graphs*, and the latter include circle*graphs*, circular-arc*graphs*, chordal*graphs*, and outerplanar*graphs*. ... A*graph*is*asteroidal**triple*-*free*(AT-*free*) if it contains no*asteroidal**triple*. ...
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