Optimal node ranking of trees in linear time
Information Processing Letters
European Journal of Combinatorics
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Duality theorems for finite structures (characterising gaps and good characterisations)
Journal of Combinatorial Theory Series B
Invitation to Discrete Mathematics
Invitation to Discrete Mathematics
Universal H-colorable graphs without a given configuration
Discrete Mathematics
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
On the order of countable graphs
European Journal of Combinatorics
Excluding any graph as a minor allows a low tree-width 2-coloring
Journal of Combinatorial Theory Series B
Universal partial order represented by means of oriented trees and other simple graphs
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
Homomorphism preservation theorems
Journal of the ACM (JACM)
Finite Automata, Digraph Connectivity, and Regular Expression Size
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
New Results on the Complexity of Oriented Colouring on Restricted Digraph Classes
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
European Journal of Combinatorics
Bounds on Edge Colorings with Restrictions on the Union of Color Classes
SIAM Journal on Discrete Mathematics
European Journal of Combinatorics
Discrete Applied Mathematics
LIFO-search on digraphs: a searching game for cycle-rank
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Characterisations and examples of graph classes with bounded expansion
European Journal of Combinatorics
Universal structures and the logic of forbidden patterns
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Type inference and type checking for queries over execution traces
The VLDB Journal — The International Journal on Very Large Data Bases
Forbidden graphs for tree-depth
European Journal of Combinatorics
Forward analysis of depth-bounded processes
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Unique-maximum and conflict-free coloring for hypergraphs and tree graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
LIFO-search: A min-max theorem and a searching game for cycle-rank and tree-depth
Discrete Applied Mathematics
Where First-Order and Monadic Second-Order Logic Coincide
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
When trees grow low: shrubs and fast MSO1
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Hypertree-depth and minors in hypergraphs
Theoretical Computer Science
Forbidden subgraph colorings and the oriented chromatic number
European Journal of Combinatorics
On tractable parameterizations of graph isomorphism
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
The fine classification of conjunctive queries and parameterized logarithmic space complexity
Proceedings of the 32nd symposium on Principles of database systems
Top-k queries over web applications
The VLDB Journal — The International Journal on Very Large Data Bases
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
On the tree-depth of random graphs
Discrete Applied Mathematics
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We define the notions tree-depth and upper chromatic number of a graph and show their relevance to local-global problems for graph partitions. In particular we show that the upper chromatic number coincides with the maximal function which can be locally demanded in a bounded coloring of any proper minor closed class of graphs. The rich interplay of these notions is applied to a solution of bounds of proper minor closed classes satisfying local conditions. In particular, we prove the following result:For every graph M and a finite set F of connected graphs there exists a (universal) graph U = U(M, F) ∈ Forbh(F) such that any graph G ∈ Forbh(F) which does not have M as a minor satisfies G → U (i.e. is homomorphic to U).This solves the main open problem of restricted dualities for minor closed classes and as an application it yields the bounded chromatic number of exact odd powers of any graph in an arbitrary proper minor closed class. We also generalize the decomposition theorem of DeVos et al. [M. DeVos, G. Ding, B. Oporowski, D.P. Sanders, B. Reed, P. Seymour, D. Vertigan, Excluding any graph as a minor allows a low tree-width 2-coloring, J. Combin. Theory Ser. B 91 (2004) 25-41].