Titlebook: ;

我悲伤

Crossing Numbers and Parameterized Complexityizing the odd crossing number of . that uses at most 9. crossings, where . is the odd crossing number of .. As a consequence of this and a result of Grohe we can show that the odd crossing number is fixed-parameter tractable.

金哥占卜者

载货清单

auxiliary

Focus-Words

Polynomial Area Bounds for MST Embeddings of Treesng tree in the Euclidean plane. They derived area bounds of . for trees of height . and conjectured that an improvement below .. ×.. is not possible for some constant . > 0. We partially disprove this conjecture by giving polynomial area bounds for arbitrary trees of maximal degree 3 and 4.

Gum-Disease

Moving Vertices to Make Drawings Planekly as possible by moving vertices. In this paper we investigate the related problem . which asks for the minimum number of vertex moves. First, we show that . is NP-hard and hard to approximate. Second, we establish a connection to the graph-drawing problem ., which yields similar results for that

GLARE

Point-Set Embedding of Trees with Edge Constraintsinct point of .. A . is a point-set embedding with no edge bends. This paper studies the following problem: The input is a set . of . points, a planar graph . with . vertices, and a geometric point-set embedding of a subgraph .′ ⊂ . on a subset of .. The desired output is a point-set embedding of .

peptic-ulcer

象形文字

The Complexity of Several Realizability Problems for Abstract Topological Graphslane in such a way that each pair of edges from . crosses exactly once and no other pair crosses. We present a polynomial algorithm which decides whether a given complete AT-graph is simply realizable. On the other hand, we show that other similar realizability problems for (complete) AT-graphs are

facetious

Efficient Extraction of Multiple Kuratowski Subdivisionsdern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., Branch-and-Cut algorithms which require multiple such subdi