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### On dominating set polyhedra of circular interval graphs [article]

Silvia Bianchi, Graciela Nasini, Paola Tolomei, Luis Miguel Torres
2018 arXiv   pre-print
These results also provide linear descriptions of polyhedra associated with several variantsof the dominating set problem on circular interval graphs.  ...  Eisenbrand et al. take advantage of this relationship to propose a complete linear description of the stable set polytope on circular interval graphs.  ...  Acknowledgements We thank Gianpaolo Oriolo and Gautier Stauffer for earlier discussions that motivated our work on this topic.  ...

### Page 8624 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews
the number of edges, plus the number of distinguished cy- cles, minus the number of distinguished polyhedra, and so on, always equals one.  ...  Summary: “The intersection graph of a family of arcs on a cir- cle is called a circular-are graph.  ...

### Distributive lattices, polyhedra, and generalized flows

Stefan Felsner, Kolja Knauer
2011 European journal of combinatorics (Print)
In other words, the point set of a D-polyhedron forms a distributive lattice with the dominance order. We provide a full characterization of the bounding hyperplanes of D-polyhedra.  ...  In fact with a D-polyhedron we associate a directed graph with arc-parameters, such that points in the polyhedron correspond to a vertex potentials on the graph.  ...  Distributive polyhedra are abbreviated D-polyhedra. Denote by ≤ dom the dominance order on R n , i.e., dominance order x ≤ dom y ⇐⇒ x i ≤ y i for all 1 ≤ i ≤ n.  ...

### Distributive Lattices, Polyhedra, and Generalized Flow [article]

S. Felsner, K. Knauer
2008 arXiv   pre-print
In other words, the point set of a D-polyhedron forms a distributive lattice with the dominance order. We provide a full characterization of the bounding hyperplanes of D-polyhedra.  ...  Aside from being a nice combination of geometric and order theoretic concepts, D-polyhedra are a unifying generalization of several distributive lattices which arise from graphs.  ...  Distributive polyhedra are abbreviated D-polyhedra. Denote by ≤ dom the dominance order on R n , i.e., dominance order x ≤ dom y ⇐⇒ x i ≤ y i for all 1 ≤ i ≤ n.  ...

### The stable set polytope of quasi-line graphs

Friedrich Eisenbrand, Gianpaolo Oriolo, Gautier Stauffer, Paolo Ventura
2008 Combinatorica
In this paper, we give a proof of the Ben Rebea conjecture by showing that it also holds for fuzzy circular interval graphs.  ...  Our result builds upon an algorithm of Bartholdi, Orlin and Ratliff which is concerned with integer programs defined by circular ones matrices.  ...  Circular Interval Graphs A circular interval graph [6] G = (V, E) is defined by the following construction, see Figure 1 : Take a circle C and a set of vertices V on the circle.  ...

### The two variable per inequality abstract domain

Axel Simon, Andy King
2010 Higher-Order and Symbolic Computation
The domain represents a sweet-point in the performance-cost tradeoff between the faster Octagon domain and the more expressive domain of general convex polyhedra.  ...  This so-called weakly-relational domain is able to express systems of linear inequalities where each inequality has at most two variables.  ...  We would like to thank the anonymous reviewers for their comments; in particular one reviewer who alerted us to Prop. 4 which incorrectly stated in [72] .  ...

### Domination When the Stars Are Out [article]

Danny Hermelin and Matthias Mnich and Erik Jan van Leeuwen and Gerhard Woeginger
2019 arXiv   pre-print
To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that exclude K_1,4 as an induced subgraph (K_1,4-free graphs).  ...  To complement that result, we show that Connected Dominating Set has no polynomial kernel on claw-free graphs and is not fixed-parameter tractable on K_1,4-free graphs.  ...  Circular and Linear Interval Trigraphs We show that if a thickening of a circular or linear interval graph has no proper W-join, then it is a proper circular-arc or proper interval graph, respectively.  ...

### Sparse Arrangements and the Number of Views of Polyhedral Scenes

Mark de Berg, Dan Halperin, Mark Overmars, Marc van Kreveld
1997 International journal of computational geometry and applications
Given a polyhedral terrain with n edges and vertices, we derive an upper bound O(n 5 2 c p log n ) on the maximum number of views of the terrain from in nity, where c is some positive constant.  ...  We show that this type of arrangements (sparse arrangements) is relevant to the study of the maximum number of topologically di erent views of a polyhedral terrain.  ...  Acknowledgement The authors thank Pankaj Agarwal for pointing out an error in Section 3 in an earlier draft of the paper. We also thank two anonymous referees for many helpful comments.  ...

### Parameterized Complexity of Induced Graph Matching on Claw-Free Graphs [article]

Danny Hermelin and Matthias Mnich and Erik Jan van Leeuwen
2014 arXiv   pre-print
Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs.  ...  In particular, we show that Independent Set is W[1]-hard on K_1,4-free graphs.  ...  Acknowledgements We thank the anonymous reviewers for helpful remarks improving the presentation of this manuscript.  ...

### Characterizing Noninteger Polyhedra with 0–1 Constraints [chapter]

András Sebő
1998 Lecture Notes in Computer Science
We characterize when the intersection of a set-packing and a set-covering polyhedron or of their corresponding minors has a noninteger vertex.  ...  an ideal polyhedron has a noninteger vertex, then they have minors whose intersection's coefficient matrix is the incidentce matrix of an odd circuit graph.  ...  Hence minors of set-packing or set-covering polyhedra are of the same type.  ...

### Combinatorics encoding geometry: the legacy of Bill Thurston in the story of one theorem [article]

Philip L. Bowers
2020 arXiv   pre-print
of Three-Manifolds.  ...  This article presents a whirlwind tour of some results surrounding the Koebe-Andre'ev-Thurston Theorem, Bill Thurston's seminal circle packing theorem that appears in Chapter 13 of The Geometry and Topology  ...  It has been a pleasure for me to review the impact derived from this one beautiful little gem of Thurston.  ...

### Master index

2002 Discrete Mathematics
Muntaner-Batle, The place of super edge-magic labelings among other classes of labelings 231 (2001) 153}168 Fischermann, M., Block graphs with unique minimum dominating sets (Note) 240 (2001) 247}251 Fitzpatrick  ...  Mandrescu, On the structure of -stable Ling, A.C.H., see J.H. Dinitz 232 (2001) 109}112 Liu, D.D.-F., Hamiltonicity and circular distance two Loebl, M. and M.  ...

### Cumulative index volumes 1–92

2000 Discrete Applied Mathematics
Santoro, Symmetries and sense of direction in labeled graphs 87 (1-3) (1998) 99-l 15 Flotow, C., On powers of m-trapezoid graphs 63 (2) (1995) 187-192 Flotow, C., On powers of circular arc graphs and proper  ...  circular arc graphs 69 (3) (1996) 197-205 Fogelman, F., E.  ...