A certifying algorithm is an algorithm that produces, with each output, a certificate or witness
(easy-to-verify proof) that the particular output has not been compromised by a bug. A user …

Let us start with two examples. A company has a machine which drills holes into printed
circuit boards. Since it produces many of these boards it wants the machine to complete one …

If a graph has bounded clique number and sufficiently large chromatic number, what can we
say about its induced subgraphs? András Gyárfás made a number of challenging …

Mathematical software and graph-theoretical algorithmic packages to efficiently model,
analyze, and query graphs are crucial in an era where large-scale spatial, societal, and …

The study of graph structure has advanced in recent years with great strides: finite graphs
can be described algebraically, enabling them to be constructed out of more basic elements …

A kernel of a directed graph D is defined as an independent set which is reachable from
each outside vertex by an arc. A graph G is called kernel-solvable if an orientation D of G …

The defining characteristic of fixed interval scheduling problems is that each job has a finite
number of fixed processing intervals. A job can be processed only in one of its intervals on …

There is a great variety of colouring concepts and results in the literature. Here our focus is
to survey results on vertex colourings of graphs defined in terms of forbidden induced …

Induced subgraphs of graphs with large chromatic number. I. Odd holes - ScienceDirect Skip to
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We consider new parameterizations of NP-optimization problems that have nontrivial lower
and/or upper bounds on their optimum solution size. The natural parameter, we argue, is the …