Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Merino, Criel"'
The weighted transition polynomial of a multimatroid is a generalization of the Tutte polynomial. By defining the activity of a skew class with respect to a basis in a multimatroid, we obtain an activities expansion for the weighted transition polyno
Externí odkaz:
http://arxiv.org/abs/2408.05046
Motivated by the appearance of embeddings in the theory of chip firing and the critical group of a graph, we introduce a version of the critical group (or sandpile group) for combinatorial maps, that is, for graphs embedded in orientable surfaces. We
Externí odkaz:
http://arxiv.org/abs/2308.13342
The anti-Ramsey number of Erd\"os, Simonovits and S\'os from 1973 has become a classic invariant in Graph Theory. To study this invariant in Matroid Theory, we use a related invariant introduce by Arocha, Bracho and Neumann-Lara. The heterochromatic
Externí odkaz:
http://arxiv.org/abs/1708.08562
The width of a delta-matroid is the difference in size between a maximal and minimal feasible set. We give a Rough Structure Theorem for delta-matroids that admit a twist of width one. We apply this theorem to give an excluded minor characterisation
Externí odkaz:
http://arxiv.org/abs/1705.09129
Publikováno v:
European Journal of Combinatorics 60:10-20. February 2017
We develop some basic tools to work with representable matroids of bounded tree-width and use them to prove that, for any prime power $q$ and constant $k$, the characteristic polynomial of any loopless, $GF(q)$-representable matroid with tree-width $
Externí odkaz:
http://arxiv.org/abs/1703.02393
Autor:
Glass, Darren, Merino, Criel
In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group $D_n$. In particular, we show that if the orbits of the $D_n$-action all have either $n$ or $2n$ points then the critical group
Externí odkaz:
http://arxiv.org/abs/1304.6011
Publikováno v:
In AKCE International Journal of Graphs and Combinatorics December 2019 16(3):319-323
The Tutte polynomial of a graph or a matroid, named after W. T. Tutte, has the important universal property that essentially any multiplicative graph or network invariant with a deletion and contraction reduction must be an evaluation of it. The dele
Externí odkaz:
http://arxiv.org/abs/1203.0090
We give two proofs that the $h$-vector of any paving matroid is a pure O-sequence, thus answering in the affirmative a conjecture made by R. Stanley, for this particular class of matroids. We also investigate the problem of obtaining good lower bound
Externí odkaz:
http://arxiv.org/abs/1008.2031