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Bounded bitolerance digraphs

2000
*
Discrete Mathematics
*

We characterize the class of

doi:10.1016/s0012-365x(99)00220-4
fatcat:ckboonabdzd63d5o3cmtvlvwru
*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*. ...##
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Tolerance Graphs
[chapter]

2013
*
Discrete Mathematics and Its Applications
*

graphs and orders , 109
block, 243

doi:10.1201/b16132-66
fatcat:j2i3oyr2e5au7mtjsdmhmcaezm
*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*...##
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Cliques that are tolerance digraphs

1997
*
Discrete Applied Mathematics
*

In this paper, we study directed graph versions of tolerance graphs, in particular. the class of totally

doi:10.1016/s0166-218x(97)00019-x
fatcat:verssjegm5gfbcoyulaeebmiem
*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. ...##
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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. ...

##
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Proper and unit bitolerance orders and graphs

1998
*
Discrete Mathematics
*

A

doi:10.1016/s0012-365x(97)00043-5
fatcat:umugguvcdvam5o4ye7bhppe3da
*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. ...##
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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*. ...##
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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*...##
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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*. ...##
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Index

2000
*
Discrete Mathematics
*

Trenk,

doi:10.1016/s0012-365x(00)00038-8
fatcat:y7nkgmuj7jdelkiexh2ythrobm
*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. ...##
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Generalized dynamic storage allocation

2014
*
Discrete Mathematics & Theoretical Computer Science
*

We find linear

doi:10.46298/dmtcs.2083
fatcat:zfe524skfzaw5oz4c4woggbmti
*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? ...##
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Veto Interval Graphs and Variations
[article]

2018
*
arXiv
*
pre-print

If you direct the edges of a point-core

arXiv:1709.09259v2
fatcat:5h2zjm5vyfggngsvy2uky7bpke
*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. ...##
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Index

2000
*
Discrete Mathematics
*

Trenk,

doi:10.1016/s0012-365x(00)00198-9
fatcat:pvoli2nzdrc6fjmljo5e2gmmky
*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. ...##
###
Master index of volumes 181–190

1998
*
Discrete Mathematics
*

Cairnie
188 (1998)
Galeana-Sfinchez, H., Kernels in edge-colored

doi:10.1016/s0012-365x(98)90328-4
fatcat:s2tsivncvfcilf6jlbl4fx24zq
*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. ...##
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On the Kernel and Related Problems in Interval Digraphs
[article]

2021
*
arXiv
*
pre-print

We observe that several of these classes, like interval catch

arXiv:2107.08278v2
fatcat:x25a2rafafhcbnc5gtpm7rsyoy
*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 ...##
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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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