## 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...