Results 51 to 60 of about 605,731 (305)
Rational exponents in extremal graph theory [PDF]
, 2016 Given a family of graphs H, the extremal number ex(n,H) is the largest m for which there exists a graph with n vertices and m edges containing no graph from the family H as a subgraph.
David Conlon +6 more
core +1 more source
Zeroth-order general Randić index of cactus graphs
AKCE International Journal of Graphs and Combinatorics, 2019 A connected graph G is said to be cactus if no two cycles of G have any common edge. The present note is devoted to developing some extremal results for the zeroth-order general Randić index of cactus graphs and finding some sharp bounds on this index ...
Hassan Ahmed +2 more
doaj +2 more sources
Emerging experimental and computational methods for studying redox‐regulated structural transitions
FEBS Letters, EarlyView.Redox reactions can reshape proteins and alter how they behave in cells, with important consequences for health and disease. This review explores emerging experimental and computational approaches for discovering these redox‐sensitive protein switches, revealing their structural effects, and predicting their behavior, opening new opportunities to ...
Tasneem Rass +2 more
wiley +1 more source
Dense H-free graphs are almost (Χ(H)-1)-partite [PDF]
, 2010 By using the Szemeredi Regularity Lemma, Alon and Sudakov recently extended the classical Andrasfai-Erdos-Sos theorem to cover general graphs. We prove, without using the Regularity Lemma, that the following stronger statement is true.
Peter Allen, Allen, Peter
core
Molecular Oncology, EarlyView.Single‐cell DNA methylation (scDNAme) profiling maps epimutational clonal evolution, revealing mechanisms of malignancy and therapeutic resistance across diverse cancer types. By providing a high‐resolution landscape of intratumoral heterogeneity, these technologies empower precise patient stratification, guide the development of enhanced ...
Ik Soo Kim
wiley +1 more source
Exact solutions to the Erdős-Rothschild problem
Forum of Mathematics, SigmaLet $\boldsymbol {k} := (k_1,\ldots ,k_s)$ be a sequence of natural numbers. For a graph G, let $F(G;\boldsymbol {k})$ denote the number of colourings of the edges of G with colours $1,\dots ,s$ such that, for every $c \in \{1 ...
Oleg Pikhurko, Katherine Staden
doaj +1 more source
AKCE International Journal of Graphs and Combinatorics, 2017 The extremal number or simply denotes the maximal number of edges in a graph on vertices with forbidden subgraphs and . The exact number of is only known for up to and . There are upper and lower bounds of for other values of .
Novi H. Bong
doaj +1 more source
On Hamiltonian Cycles in Claw-Free Cubic Graphs
Discussiones Mathematicae Graph Theory, 2022 We show that every claw-free cubic graph of order n at least 8 has at most 2⌊n4⌋{2^{\left\lfloor {{n \over 4}} \right\rfloor }} Hamiltonian cycles, and we also characterize all extremal graphs.
Mohr Elena, Rautenbach Dieter
doaj +1 more source
Spatial biology in cancer epigenetics
Molecular Oncology, EarlyView.Spatial epigenomics combines molecular profiling with tissue architecture to reveal how gene regulation is organized within intact tissues. In cancer, these technologies uncover the mechanisms driving tumor heterogeneity and microenvironmental interactions, opening new opportunities for biomarker discovery and precision medicine.
Eva Crespo‐García, Manel Esteller
wiley +1 more source
Commuting graphs and extremal centralizers
Ars Mathematica Contemporanea, 2013 We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra M n ( F ) over an arbitrary field F . It is known that if F is an algebraically closed field and n ≥ 3 , then the diameter of the commuting graph of M n ( F ) is always equal to four.
Dolinar, Gregor +3 more
openaire +5 more sources