Results 51 to 60 of about 3,613,364 (137)

Random Turán Problems for Hypergraph Expansions

Random Structures &Algorithms, Volume 69, Issue 4, December 2026.
ABSTRACT Given an r0$$ {r}_0 $$‐uniform hypergraph F$$ F $$, we define its r$$ r $$‐uniform expansion F(r)$$ {F}^{(r)} $$ to be the hypergraph obtained from F$$ F $$ by inserting r−r0$$ r-{r}_0 $$ distinct vertices into each edge of F$$ F $$, and we define ex(Gn,pr,F(r))$$ \mathrm{ex}\left({G}_{n,p}^r,{F}^{(r)}\right) $$ to be the largest F(r)$$ {F ...
Jiaxi Nie, Sam Spiro
wiley   +1 more source

Lower Bounds for Maximum Weight Bisections of Weighted Triangle‐Free Subcubic Graphs

Journal of Graph Theory, Volume 113, Issue 2, Page 252-273, October 2026.
ABSTRACT A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge‐weighted triangle‐free subcubic graphs and show that every weighted triangle‐free subcubic graph G = ( V , E , w ) Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou   +3 more
wiley   +1 more source

On the Local Resilience of Random Geometric Graphs With Respect to Connectivity and Long Cycles

Random Structures &Algorithms, Volume 69, Issue 3, October 2026.
ABSTRACT Given an increasing graph property 𝒫, a graph G$$ G $$ is α$$ \alpha $$‐resilient with respect to 𝒫 if, for every spanning subgraph H⊆G$$ H\subseteq G $$ where each vertex keeps more than a (1−α)$$ \left(1-\alpha \right) $$‐proportion of its neighbors, H$$ H $$ has property 𝒫.
Alberto Espuny Díaz, Lyuben Lichev, Alexandra Wesolek   +2 more
wiley   +1 more source

Pairs of forbidden class of subgraphs concerning $K_{1,3}$ and P₆ to have a cycle containing specified vertices [PDF]

, 2009
In [3], Faudree and Gould showed that if a 2-connected graph contains no $K_{1,3}$ and P₆ as an induced subgraph, then the graph is hamiltonian. In this paper, we consider the extension of this result to cycles passing through specified vertices.
Tsugaki, Masao, Sugiyama, Takeshi
core   +1 more source

Characterization and recognition of edge intersection graphs of 3-chromatic hypergraphs with multiplicity at most than two in the class of split graphs

Журнал Белорусского государственного университета: Математика, информатика, 2018
Let Lm(k) denote the class of edge intersection graphs of k-chromatic hypergraphs with multiplicity at most m. It is known that the problem of recognizing graphs from L1(k) is polynomially solvable if k = 2 and is NP-complete if k = 3.
Tatiana V. Lubasheva, Yury M. Metelsky
doaj  

DP-4-Colorability on Planar Graphs Excluding 7-Cycles Adjacent to 4- or 5-Cycles

Mathematics
In order to resolve Borodin’s Conjecture, DP-coloring was introduced in 2017 to extend the concept of list coloring. In previous works, it is proved that every planar graph without 7-cycles and butterflies is DP-4-colorable.
Fan Yang, Xiangwen Li, Ziwen Huang
doaj   +1 more source

Equivalence between Erdős–Hajnal and polynomial Rödl and Nikiforov conjectures

Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.
Abstract It is well‐known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erdős–Hajnal conjecture. In this note, we prove that these three conjectures are in fact equivalent, extending several previous particular results in this direction by Fox, Nguyen ...
Matija Bucić, Jacob Fox, Huy Tuan Pham
wiley   +1 more source

Flips in colorful triangulations

Journal of Computational Geometry
The associahedron is the graph $\mathcal{G}_N$ that has as nodes all triangulations of a convex $N$-gon, and an edge between any two triangulations that differ in a flip operation.
Rohan Acharya, Torsten Mütze, Francesco Verciani   +2 more
doaj   +1 more source

Simonovits's theorem in random graphs

Proceedings of the London Mathematical Society, Volume 133, Issue 4, October 2026.
Abstract Let H$H$ be a graph with χ(H)=r+1$\chi (H) = r+1$. Simonovits's theorem states that, if H$H$ is edge‐critical, the unique largest H$H$‐free subgraph of Kn$K_n$ is its largest r$r$‐partite subgraph, provided that n$n$ is sufficiently large. We show that the same holds with Kn$K_n$ replaced by the binomial random graph Gn,p$G_{n,p}$ whenever H$H$
Ilay Hoshen, Wojciech Samotij
wiley   +1 more source

Signed Projective Cubes, a Homomorphism Point of View

Journal of Graph Theory, Volume 113, Issue 1, Page 38-56, September 2026.
ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen, Reza Naserasr, Alessandra Sarti   +2 more
wiley   +1 more source