AbstractRayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using the Jacobi Identity and the all-minors matrix tree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G, we define the Rayleigh monotonicity of the generating polynomial for the set of bases of a matroid and suggest a few related problems
AbstractIt is shown that Bondy's degree condition for n-connectedness of a graph is the strongest mo...
Matroids are combinatorial objects that capture abstractly the essence of dependence. The Tutte poly...
International audienceThe ‘All Minors Matrix Tree Theorem’ (Chen, Applied Graph Theory, Graphs and E...
We prove the complete monotonicity on (0,∞)n(0,∞)n for suitable inverse powers of the spanning-tree ...
Abstract. The classical matrix tree theorem relates the number of spanning trees of a connected grap...
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in ...
AbstractKishi and Kajitani introduced the concepts of the principal partition of a graph and maximal...
In this article we establish relationships between Leavitt path algebras, talented monoids and the a...
We show that enumerating all minimal spanning and connected subsets of a given matroid is quasi-poly...
International audienceAdapting the method introduced in Graph Minors X, we propose a new proof of th...
In this work, we studied the class of lattice path matroids $\mathcal{L}$, which was first introduce...
AbstractAdapting the method introduced in Graph Minors X, we propose a new proof of the duality betw...
This book focuses on some of the main notions arising in graph theory, with an emphasis throughout o...
Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chor...
We consider a generalisation of the classical Ramsey theory setting to a setting where each of the e...
AbstractIt is shown that Bondy's degree condition for n-connectedness of a graph is the strongest mo...
Matroids are combinatorial objects that capture abstractly the essence of dependence. The Tutte poly...
International audienceThe ‘All Minors Matrix Tree Theorem’ (Chen, Applied Graph Theory, Graphs and E...
We prove the complete monotonicity on (0,∞)n(0,∞)n for suitable inverse powers of the spanning-tree ...
Abstract. The classical matrix tree theorem relates the number of spanning trees of a connected grap...
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in ...
AbstractKishi and Kajitani introduced the concepts of the principal partition of a graph and maximal...
In this article we establish relationships between Leavitt path algebras, talented monoids and the a...
We show that enumerating all minimal spanning and connected subsets of a given matroid is quasi-poly...
International audienceAdapting the method introduced in Graph Minors X, we propose a new proof of th...
In this work, we studied the class of lattice path matroids $\mathcal{L}$, which was first introduce...
AbstractAdapting the method introduced in Graph Minors X, we propose a new proof of the duality betw...
This book focuses on some of the main notions arising in graph theory, with an emphasis throughout o...
Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chor...
We consider a generalisation of the classical Ramsey theory setting to a setting where each of the e...
AbstractIt is shown that Bondy's degree condition for n-connectedness of a graph is the strongest mo...
Matroids are combinatorial objects that capture abstractly the essence of dependence. The Tutte poly...
International audienceThe ‘All Minors Matrix Tree Theorem’ (Chen, Applied Graph Theory, Graphs and E...
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