Concept

Petersen graph

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When will the zebra mussel reach Florence? A model for the spread of Dreissena polymorpha in the Arno water system (Italy)

Lorenzo Mari, Marino Gatto

The zebra mussel (Dreissena polymorpha) is a freshwater bivalve that has caused dramatic ecological and economic impacts worldwide in the last decades. Its success as ecosystem invader is mainly due to the species ability of spreading along rivers, togethe ...

2009

On the inapproximability of independent domination in 2P3-free perfect graphs

Dominique de Werra

We consider the complexity of approximation for the INDEPENDENT DOMINATING SET problem in 2P(3)-free graphs, i.e., graphs that do not contain two disjoint copies of the chordless path on three vertices as all induced subgraph. We show that, if P not equal ...

2009

Coloring Fuzzy Circular Interval Graphs

Friedrich Eisenbrand, Martin Niemeier

Computing the weighted coloring number of graphs is a classical topic in combinatorics and graph theory. Recently these problems have again attracted a lot of attention for the class of quasi-line graphs and more specifically fuzzy circular interval graphs ...

Elsevier2009

Optimistic chordal coloring: a coalescing heuristic for SSA form programs

Paolo Ienne, Philip Brisk, Ajay Kumar Verma

The interference graph for a procedure in Static Single Assignment (SSA) Form is chordal. Since the k-colorability problem can be solved in polynomial-time for chordal graphs, this result has generated interest in SSA-based heuristics for spilling and coal ...

Springer US2009

Automated Delineation of Dendritic Networks in Noisy Image Stacks

Pascal Fua, François Fleuret, Germán González Serrano

We present a novel approach to 3D delineation of dendritic networks in noisy image stacks. We achieve a level of automation beyond that of state-of-the-art systems, which model dendrites as continuous tubular structures and postulate simple appearance mode ...

Springer-Verlag2008

Polar cographs

Dominique de Werra, Tinaz Ekim

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite grap ...

Elsevier2008

Drawing cubic graphs with at most five slopes

János Pach, Balázs Keszegh

We show that every graph G with maximum degree three has a straight-line drawing in the plane using edges of at most five different slopes. Moreover, if G is connected and has at least one vertex of degree less than three, then four directions suffice. ...

2008

Complexity of mixed graph coloring

Bernard Ries

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both

\mathcal{NP}

-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...

2008

Parity-regular Steinhaus graphs

Maxime Augier

Steinhaus graphs on n vertices are certain simple graphs in bijective correspondence with binary {0,1}-sequences of length n-1. A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic ...

American Mathematical Society2008

Wavelets on Graphs via Spectral Graph Theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the sp ...

2008

Complexity of mixed graph coloring

Bernard Ries

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both

\mathcal{NP}

-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...

2008