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Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...
We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends pe ...
We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, I ...
Approximate graph matching (AGM) refers to the problem of mapping the vertices of two structurally similar graphs, which has applications in social networks, computer vision, chemistry, and biology. Given its computational cost, AGM has mostly been limited ...
A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are mini ...
A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new verte ...
Multiscale representations such as the wavelet transform are useful for many signal processing tasks. Graphs are flexible models to represent complex networks and a spectral graph wavelet transform (SGWT) has recently been developed as a generalization of ...
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We consider graphs that admit polyline drawings where all crossings occur at the same angle alpha is an element of (0, pi/2]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This r ...
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 ...
