Related papers: Four proofs of the directed Brooks' Theorem

The celebrated Erd\H{o}s-P\'osa theorem states that every undirected graph that does not admit a family of $k$ vertex-disjoint cycles contains a feedback vertex set (a set of vertices hitting all cycles in the graph) of size $O(k \log k)$.…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

We give a proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns giving them…

We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We also propose some possible research problems at the end of…

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

We introduce four new elementary short proofs of the famous K\"onig's theorem which characterizes bipartite graphs by absence of odd cycles.

The predicate complementary to the well-known Godel's provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness…

In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to…

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…

This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed…

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.

We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.

In this short note we give counterexamples to several results related to extension theorems published recently.

We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)