A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, the terminology " module " not only captures the classical graph modules but also allows to handle 2−connected components, star-cutsets, and other vertex subse...

A fast algorithm(fade) for the 2D drawing, geometric clustering and multilevel viewing of large undirected graphs is presented. The algorithm is an extension of the Barnes-Hut hierarchical space decomposition method, which includes edges and multilevel visual abstraction. Compared to the original force directed algorithm, the time overhead is O(e + n logn) where n and e are the numbers of nodes...

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, this new notion called homogeneous modules not only captures the classical graph modules but also allows to handle 2−connected components, star-cutsets, and ot...

Rent's rule and related concepts of connectivity such as dimensionality, line-length distributions, and separators have found great use in fundamental studies of di erent interconnection media, including superconductors and optics, as well as the study of optoelectronic computing systems. In this paper generalizations for systems for which the Rent exponent is not constan tthroughout the interc...

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and 2−structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomial-time algorithms are provided for: non-trivial umodule test, maximal umodule computation, and decomposition tree computation ...

We prove that the Petersen colouring conjecture implies a conjecture of Markström saying that the line graph of every bridgeless cubic graph is decomposable into cycles of even length. In addition, we describe two infinite families of 4regular graphs: the first family consists of 3-connected graphs with no even cycle decomposition and the second one consists of 4-connected signed graphs with no...

We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and 2−structures. We show that, under some axioms, a unique decomposition tree exists for umodules. Polynomial-time algorithms are provided for: non-trivial umodule test, maximal umodule computation, and decomposition tree computation ...

We consider the question whether an infinite eulerian graph has a decomposition into circuits and rays if the graph has only finitely many, say n, vertices of infinite degree, and only finitely many finite components after the removal of the vertices of infinite degree. It is known that the answer is affirmative for n < 2 and negative for n > 4. We settle the remaining case n = 3, showing that ...

In this note, I discuss a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories. This dual version of the ribbon graph decomposition is a compact orbi-cell complex with a natural weak homotopy equival...

The role of graph width metrics, such as treewidth, pathwidth, and cliquewidth, is now seen as central in both algorithm design and the delineation of what is algorithmically possible. In this article we introduce a new, related, parameter for graphs, persistence. A path decomposition of width k, in which every vertex of the underlying graph belongs to at most l nodes of the path, has pathwidth...