On weakly distinguishing graph polynomials

by J. A. Makowsky and V. Rakita. On Weakly Distinguishing Graph Polynomials. Discrete Mathematics & Theoretical Computer Science (Oct. 31, 2018). arXiv: 1810.13300 [math.CO]. Submitted.

Let \(P\) be a graph polynomial. A graph \(G\) is \(P\)-unique if every graph \(H\) with \(P(G)=P(H)\) is isomorphic to \(G\). A graph \(H\) is a \(P\)-mate of \(G\) if \(P(G)=P(H)\) and \(H\) is not isomorphic to \(G\). It is a natural question to ask whether a given graph polynomial distinguishes graphs. Read more...

Types of embedded graphs and their Tutte polynomials

by S. Huggett and I. Moffatt. Math. Proc. Camb. Phil. Soc., 2018. doi. Read more...

Peer-review in a world with rational scientists

by S. Thurner and R. Hanel. European Physical Journal B, 84(4): 707-711, 2011. doi, arXiv: 1008.4324 [physics.soc-ph].

How robust is the peer-review system (as a selection mechnism of high quality papers) under the presence of rational agents i.e. referees who tend not to accept better work than their own? Read more...

Regular colored graphs of positive degree

by R. Gurau and G. Schaeffer. Ann. Inst. Henri Poincaré Comb. Phys. Interact., 3(3): 257-320, 2016. doi, arXiv: 1307.5279 [math.CO].

This article deals with the exact enumeration of rooted bipartite \((D+1)\)-regular properly edge-coloured graphs of fixed degree \(\delta\) (hereafter rooted \((D+1)\)-coloured graphs), in dimension \(D\geqslant 3\). Read more...

Random coloured complexes

In the 1970’s M. Pezzana Sulla struttura topologica delle variety compatte. Atti Sem. Mat. Fis. Univ. Modena, 23:269-277, 1974. discovered a way of coding a piecewise-linear (PL) manifold by a properly edge-coloured graph. Read more...