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Bounded bitolerance digraphs

Kenneth P. Bogart, Ann N. Trenk
2000 Discrete Mathematics  
We characterize the class of bounded bitolerance digraphs in terms of interval orders.  ...  In addition, we characterize those bounded bitolerance digraphs which arise when linear orders or weak orders are used in place of interval orders.  ...  Characterization of bounded bitolerance digraphs A graph is a bounded bitolerance graph if it is the underlying graph of a bounded bitolerance digraph.  ... 
doi:10.1016/s0012-365x(99)00220-4 fatcat:ckboonabdzd63d5o3cmtvlvwru

Tolerance Graphs [chapter]

Martin Golumbic
2013 Discrete Mathematics and Its Applications  
graphs and orders , 109 block, 243 bounded bitolerance digraph, 263, 265, 266, 268, 277, 279, 281 bounded bitolerance graph, 111 bounded bitolerance order, 110, 119, 138, 177, 178 bounded bitolerance  ...  The relationship between interval digraphs and bounded bitolerance digraphs is explored in [ST01] . 13: Polynomial time recognition algorithms are known for the classes of bounded bitolerance digraphs  ... 
doi:10.1201/b16132-66 fatcat:j2i3oyr2e5au7mtjsdmhmcaezm

Cliques that are tolerance digraphs

Randy Shull, Ann N. Trenk
1997 Discrete Applied Mathematics  
In this paper, we study directed graph versions of tolerance graphs, in particular. the class of totally bounded bitolerance digraphs and several subclasses.  ...  When the underlying graph is complete, we prove that the classes of totally bounded bitolerance digraphs and interval catch digraphs are equal, and this implies a polynomial-time recognition algorithm  ...  Recognition of a class of totally bounded bitolerance digraphs 2.1.  ... 
doi:10.1016/s0166-218x(97)00019-x fatcat:verssjegm5gfbcoyulaeebmiem

Page 4708 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
bitolerance digraphs.  ...  For digraphs whose underlying graphs are trees, we characterize the classes of unit, proper and bounded bitolerance digraphs, and note that the unit and proper classes are equal.  ... 

Proper and unit bitolerance orders and graphs

Kenneth P. Bogart, Garth Isaak
1998 Discrete Mathematics  
A bounded tolerance 9raph or bitolerance 9raph (also known as a trapezoid 9raph) is the incomparability graph of a bounded tolerance order or bitolerance order.  ...  A tolerance or bitolerance order is said to be bounded if no tolerance is larger than the length of the corresponding interval.  ...  tolerance order, or a bounded bitolerance order.  ... 
doi:10.1016/s0012-365x(97)00043-5 fatcat:umugguvcdvam5o4ye7bhppe3da

Page 8410 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
We characterize the class of bounded bitolerance digraphs in terms of interval orders.  ...  Rusu (F-ORLN-LI; Orléans) 2000m:05104 05C20 Bogart, Kenneth P. (1-DTM; Hanover, NH); Trenk, Ann N, (1-WLL; Wellesley, MA) Bounded bitolerance digraphs.  ... 

Page 7827 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Summary: “Interval digraphs and bounded bitolerance digraphs are two different directed graph analogues to the well-known interval graphs.  ...  Beineke (1-INPFW; Fort Wayne, IN) Graph theory 2002k:05106 2002k:05103 05C20 Shull, Randy (1-WLL-C; Wellesley, MA); Trenk, Ann N. (1-WLL; Wellesley, MA) Interval digraphs and bounded bitolerance digraphs  ... 

Page 1504 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Di- graphs of this class are known as bitolerance digraphs and are the main focus of the paper.  ...  The authors characterise bounded bitol- erance digraphs which have complete underlying graphs and this characterisation implies a polynomial time algorithm for recog- nising such digraphs.  ... 


2000 Discrete Mathematics  
Trenk, Bounded bitolerance digraphs (1}3) 13} 20 Fertig, R.A., On path-sequential labellings of cycles (1}3) 21} 32 Fertin, G., A study of minimum gossip graphs (1}3) 33} 57 Ginosar, Y. and R.  ...  Takahara, A lower bound on the probability of a "nite union of events (1}3) 147}158 KuK ndgen, A., see H. Asari (1}3) 263}264 LarrioH n, F. and V.  ... 
doi:10.1016/s0012-365x(00)00038-8 fatcat:y7nkgmuj7jdelkiexh2ythrobm

Generalized dynamic storage allocation

H. A. Kierstead, Karin R. Saoub
2014 Discrete Mathematics & Theoretical Computer Science  
We find linear bounds for the online-with-representation chromatic number of various classes of tolerance graphs and apply these results to a generalization of Dynamic Storage Allocation, giving us a polynomial  ...  The authors can also prove similar bounds for totally bounded bitolerance and point-core bitolerance graphs.  ...  Can the results on the pseudo-online chromatic number be adjusted to give bounds for the online chromatic number of bounded tolerance graphs?  ... 
doi:10.46298/dmtcs.2083 fatcat:zfe524skfzaw5oz4c4woggbmti

Veto Interval Graphs and Variations [article]

Breeann Flesch, Jessica Kawana, Joshua D. Laison, Dana Lapides, Stephanie Partlow, Gregory J. Puleo
2018 arXiv   pre-print
If you direct the edges of a point-core bitolerance graph you get a point-core bitolerance digraph, and if you then remove the loops you get an interval catch digraph, which have been studied extensively  ...  If all intervals I a in a bounded bitolerance representation R have p(a) = q(a), then R is a point-core bitolerance representation and its corresponding graph G is a point-core bitolerance graph.  ... 
arXiv:1709.09259v2 fatcat:5h2zjm5vyfggngsvy2uky7bpke


2000 Discrete Mathematics  
Trenk, Bounded bitolerance digraphs 215 (2000) 13} 20 BollobaH s, B. and D.B. West, A note on generalized chromatic number and generalized girth 213 (2000) 29} 34 BollobaH s, B. and O.  ...  Maureso, Endo-circulant digraphs of degree two and Cayley digraphs on "nite abelian groups (Note) 211 (2000) 203}208 Cai, M.-c., X. Deng and W.  ... 
doi:10.1016/s0012-365x(00)00198-9 fatcat:pvoli2nzdrc6fjmljo5e2gmmky

Master index of volumes 181–190

1998 Discrete Mathematics  
Cairnie 188 (1998) Galeana-Sfinchez, H., Kernels in edge-colored digraphs 184 (1998) Gallant, R. and C.J.  ...  Isaak, Proper and unit bitolerance orders and graphs Bohus, G., W. Jockusch, C.W. Lee and N. Prabhu, On a triangulation of the 3-ball and the solid torus (Note) Bollobfis, B. and T.  ... 
doi:10.1016/s0012-365x(98)90328-4 fatcat:s2tsivncvfcilf6jlbl4fx24zq

On the Kernel and Related Problems in Interval Digraphs [article]

Mathew C. Francis, Pavol Hell, Dalu Jacob
2021 arXiv   pre-print
We observe that several of these classes, like interval catch digraphs, interval nest digraphs, adjusted interval digraphs and chronological interval digraphs, are subclasses of the more general class  ...  A digraph G is an interval digraph if a pair of intervals (S_u,T_u) can be assigned to each vertex u of G such that (u,v)∈ E(G) if and only if S_u∩ T_v≠∅.  ...  As noted above, totally bounded bitolerance digraphs are a subclass of reflexive interval digraphs, and therefore all the results that we obtain for reflexive interval digraphs hold also for this class  ... 
arXiv:2107.08278v2 fatcat:x25a2rafafhcbnc5gtpm7rsyoy

Page 150 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Trees and cycles that are bounded bitolerance digraphs. (English summary) 97h:05072 Boudali, Benalssa (with Ille, Pierre) La morphologie des tournois.  ...  On strongly connected digraphs with bounded cycle length. (English summary) 97e:05095 Kim, Jeong Han (with Tetali, Prasad; Fishburn, Peter C.) Score certificates for tourna- ments.  ... 
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