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On claw-free asteroidal triple-free graphs
2002
Discrete Applied Mathematics
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We present an O(n 2:376 ) algorithm for recognizing 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. ...
doi:10.1016/s0166-218x(01)00208-6
fatcat:7isrygxg3ndvnpa6t5ud22bx6u
On Claw-Free Asteroidal Triple-Free Graphs
[chapter]
1999
Lecture Notes in Computer Science
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We present an O(n 2:376 ) algorithm for recognizing 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. ...
doi:10.1007/3-540-46784-x_35
fatcat:4ix47kqhenekjaqv7fsvqnihvm
Algorithms for the Recognition of Net-free Graphs and for Computing Maximum Cardinality Matchings in Claw-free Graphs
2014
Studies in Informatics and Control
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During the last decades, numerous studies have been undertaken 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. ...
doi:10.24846/v23i2y201406
fatcat:rv6tfr2t2fbpzgzr4vwkr4xm4m
Approximating the bandwidth for asteroidal triple-free graphs
[chapter]
1995
Lecture Notes in Computer Science
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Then (G) 2 implies that G is 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. ...
doi:10.1007/3-540-60313-1_161
fatcat:fe3ku6hczfhyvalakh42gx4bzy
Characterising AT-free Graphs with BFS
[article]
2018
arXiv
pre-print
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An 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. ...
arXiv:1807.05065v1
fatcat:ubnc6vlmuzburj5ty5yxcx5eby
Page 4037 of Mathematical Reviews Vol. , Issue 2003f
[page]
2003
Mathematical Reviews
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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. ...
Obstructions to chordal circular-arc graphs of small independence number
2013
Electronic Notes in Discrete Mathematics
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This is akin to the notion of 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. ...
doi:10.1016/j.endm.2013.10.012
fatcat:xkph4nvkdfenvf437g4jktrnw4
On linear and circular structure of (claw, net)-free graphs
2003
Discrete Applied Mathematics
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We show also how 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. ...
doi:10.1016/s0166-218x(02)00571-1
fatcat:2pbmjgfx7zfj7hwy3cz2djmtlm
Induced matchings in asteroidal triple-free graphs
2003
Discrete Applied Mathematics
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We ÿrst deÿne a wider class of 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. ...
doi:10.1016/s0166-218x(03)00390-1
fatcat:gtwpwwjlqbg5ldlcml4ofzitwq
Contents
2003
Discrete Applied Mathematics
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Mosca
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. ...
doi:10.1016/s0166-218x(03)00587-0
fatcat:s4xzqhrk6vaq3euwplh4zfo24y
AT-free graphs: linear bounds for the oriented diameter
2004
Discrete Applied Mathematics
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Let G be a bridgeless connected undirected (b.c.u.) 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. ...
doi:10.1016/s0166-218x(03)00376-7
fatcat:hkiddpjv45dv7jvejnnc2z7lh4
Boxicity and cubicity of asteroidal triple free graphs
2010
Discrete Mathematics
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A 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. ...
doi:10.1016/j.disc.2010.01.020
fatcat:blgsakh46jdsrodwtnp4ugcaq4
Author index to volume
2003
Discrete Applied Mathematics
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Mosca, 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. ...
doi:10.1016/s0166-218x(03)00591-2
fatcat:vut2tfclizgvdnot7fn7dd4tou
Boxicity and Cubicity of Asteroidal Triple free graphs
[article]
2009
arXiv
pre-print
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Let G be an AT-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. ...
arXiv:0812.0894v2
fatcat:mnrbwranvbayhl3eq652xbffqi
Induced matchings in intersection graphs
2004
Discrete Mathematics
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In particular, we show that if G is a polygon-circle 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. ...
doi:10.1016/j.disc.2003.05.001
fatcat:glgc57tm2jd4totyihmatyv3ua
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