Information and Control - The MIT Press scientific computation series
Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Comparing queues and stacks as mechanisms for laying out graphs
SIAM Journal on Discrete Mathematics
Laying out graphs using queues
SIAM Journal on Computing
Exploring the powers of stacks and queues via graph layouts
Exploring the powers of stacks and queues via graph layouts
Homomorphisms of Edge-Colored Graphs and Coxeter Groups
Journal of Algebraic Combinatorics: An International Journal
Shallow excluded minors and improved graph decompositions
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics
Embedding Graphs into a Three Page Book with O(m log n) Crossings of Edges over the Spine
SIAM Journal on Discrete Mathematics
Colored homomorphisms of colored mixed graphs
Journal of Combinatorial Theory Series B
Which crossing number is it anyway?
Journal of Combinatorial Theory Series B
Stack and Queue Layouts of Posets
SIAM Journal on Discrete Mathematics
Separating Thickness from Geometric Thickness
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Nonrepetitive colorings of graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
Layout of Graphs with Bounded Tree-Width
SIAM Journal on Computing
Pattern avoidance: themes and variations
Theoretical Computer Science - Combinatorics on words
Embedding a Graph into a d + 1-page Book with ⌈m logd n⌉ Edge-crossings over the Spine
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Linear time low tree-width partitions and algorithmic consequences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Grad and classes with bounded expansion I. Decompositions
European Journal of Combinatorics
Grad and classes with bounded expansion II. Algorithmic aspects
European Journal of Combinatorics
Grad and classes with bounded expansion III. Restricted graph homomorphism dualities
European Journal of Combinatorics
On forbidden subdivision characterizations of graph classes
European Journal of Combinatorics
Journal of Graph Theory
The order of the largest complete minor in a random graph
Random Structures & Algorithms
The complexity of nonrepetitive coloring
Discrete Applied Mathematics
Two remarks on the Burr-Erdős conjecture
European Journal of Combinatorics
European Journal of Combinatorics
European Journal of Combinatorics
Finite model theory on tame classes of structures
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Constant-factor approximation of the domination number in sparse graphs
European Journal of Combinatorics
Testing first-order properties for subclasses of sparse graphs
Journal of the ACM (JACM)
A dynamic data structure for counting subgraphs in sparse graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Hi-index | 0.00 |
Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Nesetril and Ossona de Mendez. These classes are defined by the fact that the maximum average degree of a shallow minor of a graph in the class is bounded by a function of the depth of the shallow minor. Several linear-time algorithms are known for bounded expansion classes (such as subgraph isomorphism testing), and they allow restricted homomorphism dualities, amongst other desirable properties. In this paper, we establish two new characterisations of bounded expansion classes, one in terms of so-called topological parameters and the other in terms of controlling dense parts. The latter characterisation is then used to show that the notion of bounded expansion is compatible with the Erdos-Renyi model of random graphs with constant average degree. In particular, we prove that for every fixed d0, there exists a class with bounded expansion, such that a random graph of order n and edge probability d/n asymptotically almost surely belongs to the class. We then present several new examples of classes with bounded expansion that do not exclude some topological minor, and appear naturally in the context of graph drawing or graph colouring. In particular, we prove that the following classes have bounded expansion: graphs that can be drawn in the plane with a bounded number of crossings per edge, graphs with bounded stack number, graphs with bounded queue number, and graphs with bounded non-repetitive chromatic number. We also prove that graphs with 'linear' crossing number are contained in a topologically-closed class, while graphs with bounded crossing number are contained in a minor-closed class.