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Tolerance Graphs [chapter]

Martin Golumbic
2013 Discrete Mathematics and Its Applications  
, 66 hierarchy of φ-tolerance chain graphs, 232 of bounded bitolerance digraphs, 272 of bounded bitolerance orders, 178 of containment graphs, 219 of NeST graphs, 222 of perfect graphs, 66, 67  ...  We have presented hierarchies for the following classes of graphs and orders: Graph Classes Figure 2.  ... 
doi:10.1201/b16132-66 fatcat:j2i3oyr2e5au7mtjsdmhmcaezm

Page 8509 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
This paper compares 18 classes of bounded bitolerance orders defined by further restrictions of three types on representations.  ...  Bayer (1-KS; Lawrence, KS) 2004k:06003 06A07 05C75 Isaak, Garth (1-LEHI; Bethlehem, PA); Nyman, Kathryn L. (1-CRNL; Ithaca, NY); Trenk, Ann N. (1-WLL; Wellesley, MA) A hierarchy of classes of bounded bitolerance  ... 

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.  ...  This paper gives a general lower bound for the forced unilat- eral orientation number and shows that the unilateral orientation number of a graph of size m, order n, and having edge connec- tivity 1 is  ... 

The hierarchy of classes of bounded bitolerance orders [chapter]

Martin Charles Golumbic, Ann N. Trenk
Tolerance Graphs  
We also provide separating examples between unequal classes of bitolerance orders. Definition 2. (Unit): P is a unit bitolerance order if it has a bounded bitolerance representation Definition 3.  ...  We provide a more comprehensive list of classes of bitolerance orders and prove equality between some of these classes in general and other classes in the bipartite domain.  ...  The Hierarchy of Classes As discussed in the introduction, Figure 3 shows 18 classes of bounded bitolerance orders listed by their abbreviations from the table in Figure 2 .  ... 
doi:10.1017/cbo9780511542985.012 fatcat:3zfd7cagdnfmdflp5xbxlenlom

An Intersection Model for Multitolerance Graphs: Efficient Algorithms and Hierarchy

George B. Mertzios
2013 Algorithmica  
The author would like to thank Sagi Snir from the University of Haifa, Israel, for indicating the application of multitolerance graphs in the comparison of DNA sequences.  ...  The resulting hierarchy of classes of perfect graphs is complete, i.e. all inclusions are strict 3 . This hierarchy is presented in Figure 5 .  ...  These results complement the hierarchy of perfect graphs given in [11] . The resulting hierarchy of classes of perfect graphs is complete, i.e. all inclusions are strict. Notation.  ... 
doi:10.1007/s00453-012-9743-2 fatcat:jpkcwljv4rfbvapggypbdu5j5a

An Intersection Model for Multitolerance Graphs: Efficient Algorithms and Hierarchy [chapter]

George B. Mertzios
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
The author would like to thank Sagi Snir from the University of Haifa, Israel, for indicating the application of multitolerance graphs in the comparison of DNA sequences.  ...  The resulting hierarchy of classes of perfect graphs is complete, i.e. all inclusions are strict 3 . This hierarchy is presented in Figure 5 .  ...  These results complement the hierarchy of perfect graphs given in [11] . The resulting hierarchy of classes of perfect graphs is complete, i.e. all inclusions are strict. Notation.  ... 
doi:10.1137/1.9781611973082.100 dblp:conf/soda/Mertzios11 fatcat:5jw6735gfzgxtngovoh4ldtk6m

Page 2530 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
A hierarchy of classes of bounded bitolerance orders. (English summary) Ars Combin. 69 (2003), 33-53. (Douglas B. West) 2004k:06003 06A07 (05C75) Trenkel, C. (with Speake, C. C.)  ...  On the existence of a solution to the Cauchy problem for a first-order partial differential equation in the degenerate case. (Russian. Russian summary) Differ.  ... 

Subject Index Volumes 1–200

2001 Discrete Mathematics  
, 5326 of a linear code, 864 weight hierarchy, 4386, 4590, 5435 of codes, 5219 of semiprimitive codes, 4590 weight in a code, 67 weight of a code, 67, 75, 76, 78 word, 554 weight of a majority  ...  5167 labeled tree, 1944 order, 1177 ordered set, 1170, 3118 partially ordered free monoids, 700 poised, 4494 4319, 6023 Welsh-Powell bound, 2493 upper bound, 2493, 6015 Welter game, 2558 Welzl  ...  a bridged graph, 2465 a chordal graph, 2465 a graph, 99, 5594 a simple block, 1038 convergence, 584 the clique graph, 4633 radius two, 1005 versus diameter, 5056 Rado, 38, 226, 363, 1279 Rado, 38, 226  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Page 1085 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
A hierarchy of classes of bounded bitolerance orders. (English summary) Ars Combin. 69 (2003), 33-53. (Douglas B. West) 2004k:06003 06A07 (05C75) — (with Narayan, Darren A.)  ...  Notae 40 (1999/02), 115-121 (2004). 30045 — (with Cetin, Omer Faruk; Raina, Ravinder Krishna) On a novel class of multivalently analytic functions with negative coefficients. (English summary) J.  ...