10 research outputs found
HajĂłs' conjecture and small cycle double covers of planar graphs
AbstractWe prove that every simple even planar graph on n vertices has a partition of its edge set into at most â(n - 1)/2â cycles. A previous proof of this result was given by Tao, but is incomplete, and we provide here a somewhat different proof. We also discuss the connection between this result and the Small Cycle Double Cover Conjecture
Towards the Erd\H{o}s-Gallai Cycle Decomposition Conjecture
In the 1960's, Erd\H{o}s and Gallai conjectured that the edges of any
-vertex graph can be decomposed into cycles and edges. We improve
upon the previous best bound of cycles and edges due to
Conlon, Fox and Sudakov, by showing an -vertex graph can always be
decomposed into cycles and edges, where is the
iterated logarithm function.Comment: Final version, accepted for publicatio
Towards the ErdĆs-Gallai cycle decomposition conjecture
In the 1960's, ErdĆs and Gallai conjectured that the edges of any n-vertex graph can be decomposed into O(n) cycles and edges. We improve upon the previous best bound of O(nloglogn) cycles and edges due to Conlon, Fox and Sudakov, by showing an n-vertex graph can always be decomposed into O(nlogân) cycles and edges, where logân is the iterated logarithm function
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), Vol. IV
The fourth volume, in my book series of âCollected Papersâ, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) â but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions. This is an eclectic tome of 800 pages with papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory, information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics. It was my preoccupation and collaboration as author, co-author, translator, or cotranslator, and editor with many scientists from around the world for long time. Many topics from this book are incipient and need to be expanded in future explorations