Filters








149 Hits in 2.3 sec

On claw-free asteroidal triple-free graphs

Harald Hempel, Dieter Kratsch
2002 Discrete Applied Mathematics  
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]

Harald Hempel, Dieter Kratsch
1999 Lecture Notes in Computer Science  
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

Mihai TĂLMACIU, Victor LEPIN
2014 Studies in Informatics and Control  
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]

T. Kloks, D. Kratsch, H. Müller
1995 Lecture Notes in Computer Science  
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]

Jesse Beisegel
2018 arXiv   pre-print
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  
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

Mathew Francis, Pavol Hell, Juraj Stacho
2013 Electronic Notes in Discrete Mathematics  
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

Andreas Brandstädt, Feodor F. Dragan
2003 Discrete Applied Mathematics  
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

Jou-Ming Chang
2003 Discrete Applied Mathematics  
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  
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

Fedor V Fomin, Martı́n Matamala, Erich Prisner, Ivan Rapaport
2004 Discrete Applied Mathematics  
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

Diptendu Bhowmick, L. Sunil Chandran
2010 Discrete Mathematics  
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  
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]

Diptendu Bhowmick, L. Sunil Chandran
2009 arXiv   pre-print
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

Kathie Cameron
2004 Discrete Mathematics  
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
« Previous Showing results 1 — 15 out of 149 results