Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
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
Tree-Related Widths of Graphs and Hypergraphs
SIAM Journal on Discrete Mathematics
Grad and classes with bounded expansion III. Restricted graph homomorphism dualities
European Journal of Combinatorics
Well-Quasi-Orders in Subclasses of Bounded Treewidth Graphs
Parameterized and Exact Computation
On Digraph Width Measures in Parameterized Algorithmics
Parameterized and Exact Computation
Hi-index | 5.23 |
We introduce two new notions for hypergraphs, hypertree-depth and minors in hypergraphs. We characterise hypergraphs of bounded hypertree-depth by the ultramonotone robber and marshals game, by vertex-hyperrankings and by centred hypercolourings. Furthermore, we show that minors in hypergraphs are 'well-behaved' with respect to hypertree-depth and other hypergraph invariants, such as generalised hypertree-depth and generalised hyperpath-width. We work in the framework of hypergraph pairs(G,H), consisting of a graph G and a hypergraph H that share the same vertex set. This general framework allows us to obtain hypergraph minors, graph minors and induced graph minors as special cases.