Are motorways rational from slime mould's point of view ?
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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 ...
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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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 ...
We consider a source that transmits information to a receiver by routing it over a communication network represented by a graph and examine rate benefits that finite complexity processing at the intermediate nodes may offer. We show that there exist config ...
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 ...
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 ...
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 ...
The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...
The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. A lot of problems, which are in general NP-complete, can be solved in polynomial time for graphs with small treewidth. In the first part of this paper we presen ...
