12 research outputs found
New bounds on even cycle creating Hamiltonian paths using expander graphs
We say that two graphs on the same vertex set are -creating if their union
(the union of their edges) contains as a subgraph. Let be the
maximum number of pairwise -creating Hamiltonian paths of . Cohen,
Fachini and K\"orner proved In this paper we close the superexponential gap
between their lower and upper bounds by proving
We also improve the
previously established upper bounds on for , and we present
a small improvement on the lower bound of F\"uredi, Kantor, Monti and Sinaimeri
on the maximum number of so-called pairwise reversing permutations. One of our
main tools is a theorem of Krivelevich, which roughly states that (certain
kinds of) good expanders contain many Hamiltonian paths.Comment: 14 pages, LaTeX2e; v2: updated Footnote 1 on Page 5; v3: revised
version incorporating suggestions by the referees (the changes are mainly in
Section 5); v4: final version to appear in Combinatoric
New bounds on even cycle creating Hamiltonian paths using expander graphs
We say that two graphs on the same vertex set are -creating if their union
(the union of their edges) contains as a subgraph. Let be the
maximum number of pairwise -creating Hamiltonian paths of . Cohen,
Fachini and K\"orner proved In this paper we close the superexponential gap
between their lower and upper bounds by proving
We also improve the
previously established upper bounds on for , and we present
a small improvement on the lower bound of F\"uredi, Kantor, Monti and Sinaimeri
on the maximum number of so-called pairwise reversing permutations. One of our
main tools is a theorem of Krivelevich, which roughly states that (certain
kinds of) good expanders contain many Hamiltonian paths.Comment: 14 pages, LaTeX2e; v2: updated Footnote 1 on Page 5; v3: revised
version incorporating suggestions by the referees (the changes are mainly in
Section 5); v4: final version to appear in Combinatoric
Questions on the Structure of Perfect Matchings inspired by Quantum Physics
We state a number of related questions on the structure of perfect matchings.
Those questions are inspired by and directly connected to Quantum Physics. In
particular, they concern the constructability of general quantum states using
modern photonic technology. For that we introduce a new concept, denoted as
inherited vertex coloring. It is a vertex coloring for every perfect matching.
The colors are inherited from the color of the incident edge for each perfect
matching. First, we formulate the concepts and questions in pure
graph-theoretical language, and finally we explain the physical context of
every mathematical object that we use. Importantly, every progress towards
answering these questions can directly be translated into new understanding in
quantum physics.Comment: 10 pages, 4 figures, 6 questions (added suggestions from peer-review
AIMSurv: First pan-European harmonized surveillance of Aedes invasive mosquito species of relevance for human vector-borne diseases
Human and animal vector-borne diseases, particularly mosquito-borne diseases, are emerging or re-emerging worldwide. Six Aedes invasive mosquito (AIM) species were introduced to Europe since the 1970s: Aedes aegypti, Ae. albopictus, Ae. japonicus, Ae. koreicus, Ae. atropalpus and Ae. triseriatus. Here, we report the results of AIMSurv2020, the first pan-European surveillance effort for AIMs. Implemented by 42 volunteer teams from 24 countries. And presented in the form of a dataset named âAIMSurv Aedes Invasive Mosquito species harmonized surveillance in Europe. AIM-COST Action. Project ID: CA17108â. AIMSurv2020 harmonizes field surveillance methodologies for sampling different AIMs life stages, frequency and minimum length of sampling period, and data reporting. Data include minimum requirements for sample types and recommended requirements for those teams with more resources. Data are published as a Darwin Core archive in the Global Biodiversity Information Facility- Spain, comprising a core file with 19,130 records (EventID) and an occurrences file with 19,743 records (OccurrenceID). AIM species recorded in AIMSurv2020 were Ae. albopictus, Ae. japonicus and Ae. koreicus, as well as native mosquito species