................................................................................................................. iii ACKNOWLEDGMENTS............................................................................................ viii LIST OF TABLES.......................................................................................................... x LIST OF FIGURES ..............................

We prove that we can specify by formulas of monadic second-order logic the unique planar embedding of a 3-connected planar graph. If the planar graph is not 3-connected but given with a linear order of its set of edges, we can also define a planar embedding by monadic second-order formulas. We cannot do so in general without the ordering, even for 2-connected planar graphs. The planar embedding...

We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by crossing number k of given embedding. A graph is called if it can be drawn in plane with at most one per edge. Our recursively reduce a to 3k planar graphs, using edge removal and node contraction. main algorithm then solves FCE-MaxCut introduced Liers Pardella [23]....

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs hav...

The most frequently used language to represent the semantic graphs is the RDF (W3C standard for meta-modeling). The construction of semantic graphs is a source of numerous errors of interpretation. The processing of large semantic graphs is a limit to the use of semantics in current information systems. The work presented in this paper is part of a new research at the border between two areas: ...

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P,D, gyroid and H surfaces. Some of these graphs are natural ge...

The most frequently used language to represent the semantic graphs is the RDF (W3C standard for meta-modeling). The construction of semantic graphs is a source of numerous errors of interpretation. The processing of large semantic graphs is a limit to the use of semantics in current information systems. The work presented in this paper is part of a new research at the border between two areas: ...