Related papers: Graphs of groups and the Atiyah conjecture for one…
Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question…
This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.
This is the third of a series of four papers in which we prove the following relaxation of the Loebl-Komlos-Sos Conjecture: For every $\alpha>0$ there exists a number $k_0$ such that for every $k>k_0$ every $n$-vertex graph $G$ with at…
This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.
Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.
This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.
The paper has been withdrawn by the author.
In this paper, we are motivated by the conjectures proposed by C.~Bender \textit{et al.}, \cite{C} in 2024. We have settled the first two conjectures negatively by providing a counter example in \cite{KTJ}, whereas in this paper, we prove…
This paper has been withdrawn by the author because there is a gap in Lemma 9.
Recently in graph theory several authors have studied the spectrum of the Cayley graph of the symmetric group S_n generated by the transpositions (1, i) for 2 <= i <= n. Several conjectures were made and partial results were obtained. The…
In previous works the group inverse of a network obtained by some perturbations, as the deletion of a vertex, the addition of a new vertex, contraction of an edge, etc. is obtained in terms of the group inverse of the original network. In…
This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem. We examine two statements in graph…
This paper is withdrawn by the author due to a critical error in the proof of the main theorem, Theorem 3.10. (More specifically the identity (5.18) is incorrect in that the $T^*S^1(2)$-factor is missing in the right hand side of the…
This paper has been withdrawn by the authors, due a gap in the proof of the main Theorem.
This paper has been withdrawn by the author due to a crucial argument error at p.10.
It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of…
To a closed wide Lie subgroupoid $\mathbf{A}$ of a Lie groupoid $\mathbf{L}$, i.e. a Lie groupoid pair, we associate an Atiyah class which we interpret as the obstruction to the existence of $\mathbf{L}$-invariant fibrewise affine…
Atiyah's formulation of what is nowadays called the convexity theorem of Atiyah-Guillemin-Sternberg has two parts: (a) the image of the moment map arising from a Hamiltonian action of a torus on a symplectic manifold is a convex polytope,…