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Two vertex colorings of a graph G are equivalent if they induce the same partition of the vertex set into color classes. The graphical Bell number B(G) is the number of non-equivalent vertex colorings of G. We determine a sharp lower bound on B(G) for graphs G of order n and maximum degree n− 3, and we characterize the graphs for which the bound is attained.

- Romain Absil, Hadrien Mélot
- ArXiv
- 2013

We present Digenes, a new discovery system that aims to help researchers in graph theory. While its main task is to find extremal graphs for a given (function of) invariants, it also provides some basic support in proof conception. This has already been proved to be very useful to find new conjectures since the AutoGraphiX system of Caporossi and Hansen… (More)

- Arthur W. Chester, Romain Absil, Geoffrey J. Kennedy, Pierre Lagarde, A-M Flank
- Journal of synchrotron radiation
- 1999

- Romain Absil, Hadrien Mélot
- ArXiv
- 2013

We introduce the price of symmetrisation, a concept that aims to compare fundamental differences (gap and quotient) between values of a given graph invariant for digraphs and the values of the same invariant of the symmetric versions of these digraphs. Basically, given some invariant our goal is to characterise digraphs that maximise price of… (More)

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