8 research outputs found
A more accurate view of the Flat Wall Theorem
We introduce a supporting combinatorial framework for the Flat Wall Theorem.
In particular, we suggest two variants of the theorem and we introduce a new,
more versatile, concept of wall homogeneity as well as the notion of regularity
in flat walls. All proposed concepts and results aim at facilitating the use of
the irrelevant vertex technique in future algorithmic applications.Comment: arXiv admin note: text overlap with arXiv:2004.1269
Graph Minors and Parameterized Algorithm Design
Abstract. The Graph Minors Theory, developed by Robertson and Sey-mour, has been one of the most influential mathematical theories in pa-rameterized algorithm design. We present some of the basic algorithmic techniques and methods that emerged from this theory. We discuss its direct meta-algorithmic consequences, we present the algorithmic appli-cations of core theorems such as the grid-exclusion theorem, and we give a brief description of the irrelevant vertex technique
Contraction checking in graphs on surfaces
The CONTRACTION CHECKING problem asks, given two graphs H and G as
input, whether H can be obtained from G by a sequence of edge
contractions. Contraction Checking remains NP-complete, even when H is
fixed. We show that this is not the case when G is embeddable in a
surface of fixed Euler genus. In particular, we give an algorithm that
solves Contraction Checking in f(h, g) . |V (G)|(3) steps, where h is
the size of H and g is the Euler genus of the input graph G
Contraction checking in graphs on surfaces
The Contraction Checking problem asks, given two graphs H and G as input, whether H can be obtained from G by a sequence of edge contractions. Contraction Checking remains NP-complete, even when H is fixed. We show that this is not the case when G is embeddable in a surface of fixed Euler genus. In particular, we give an algorithm that solves Contraction Checking in f(h, g) · |V (G) | 3 steps, where h is the size of H and g is the Euler genus of the input graph G
Contraction checking in graphs on surfaces
The CONTRACTION CHECKING problem asks, given two graphs H and G as input, whether H can be obtained from G by a sequence of edge contractions. CONTRACTION CHECKING remains NP-complete, even when H is fixed. We show that this is not the case when G is embeddable in a surface of fixed Euler genus. In particular, we give an algorithm that solves CONTRACTION CHECKING in f(h,g) ·SCOPUS: cp.pinfo:eu-repo/semantics/publishe