Related papers: The step Sidorenko property and non-norming edge-t…
A bipartite graph $G$ is semi-algebraic in $\mathbb{R}^d$ if its vertices are represented by point sets $P,Q \subset \mathbb{R}^d$ and its edges are defined as pairs of points $(p,q) \in P\times Q$ that satisfy a Boolean combination of a…
The super-neighborhood of a vertex set $A$ in a graph $G$, denoted by $\Lambda^2(A)$, is the set of vertices adjacent to at least two vertices in $A$. We say that a bipartite graph $G=(X, Y)$ with $|X| \geq 2$ satisfies the double Hall…
We provide a very elementary proof of a classical extremality result due to Sidorenko (Discrete Math. 131.1-3, 1994), which states that among all connected graphs $G$ on $k$ vertices, the $k$-vertex star maximises the number of graph…
A path of a graph $G$ is called a Hamilton path if it passes through all the vertices of $G$. A graph is Hamilton-connected if any two vertices are connected by a Hamilton path. Note that any bipartite graph is not Hamilton-connected. We…
We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erd\"os-Simonovits and…
An $(a,b)$-biregular bipartite graph is a bipartite graph with bipartition $(X, Y)$ such that each vertex in $X$ has degree $a$ and each vertex in $Y$ has degree $b$. By the bipartite expander mixing lemma, biregular bipartite graphs have…
The Erd\H{o}s-Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erd\H{o}s-Simonovits type stability theorem in multi-partite graphs. Different from the Erd\H{o}s-Simonovits stability…
We study a class of determinant inequalities that are closely related to Sidorenko's famous conjecture (Also conjectured by Erd\H os and Simonovits in a different form). Our results can also be interpreted as entropy inequalities for…
We prove a far-reaching strengthening of Szemer\'edi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned into a bounded number of parts of roughly the same size such…
We find Dirac-type sufficient conditions for a hypergraph $\mathcal H$ with few edges to be hamiltonian. We also show that these conditions provide that $\mathcal H$ is {\em super-pancyclic}, i.e., for each $A \subseteq V(\mathcal H)$ with…
The \emph{Antimagic Graph Conjecture} asserts that every connected graph $G = (V, E)$ except $K_2$ admits an edge labeling such that each label $1, 2, ..., |E|$ is used exactly once and the sums of the labels on all edges incident with a…
Property $(P)$, introduced in recent work and rooted in the classical theory of Parter vertices, concerns the existence of a nonsingular matrix $A\in S(G)$ for which every vertex of $G$ is a $P$-vertex. Previous investigations have fully…
Answering a question of Simonovits and S\' os, Conlon, Fox, and Sudakov proved that for any nonempty graph $H$, and any $\varepsilon>0$, there exists $\delta>0$ polynomial in $\varepsilon$, such that if $G$ is an $n$-vertex graph with the…
We study variants of Sidorenko's conjecture in tournaments, where new phenomena arise that do not have clear analogues in the setting of undirected graphs. We first consider oriented graphs that are systematically under-represented in…
Kang and Park recently showed that every cubic (loopless) multigraph is incidence 6-choosable [On incidence choosability of cubic graphs. \emph{arXiv}, April 2018]. Equivalently, every bipartite graph obtained by subdividing once every edge…
We present a tight extremal threshold for the existence of Hamilton cycles in graphs with large minimum degree and without a large ``bipartite hole`` (two disjoint sets of vertices with no edges between them). This result extends Dirac's…
The well-known regularity lemma of E. Szemer\'edi for graphs (i.e. 2-uniform hypergraphs) claims that for any graph there exists a vertex partition with the property of quasi-randomness. We give a simple construction of such a partition. It…
As a directed analog of Sidorenko's conjecture in extremal graph theory, Fox, Himwich, Zhou, and the second author defined an oriented graph $H$ to be tournament Sidorenko (anti-Sidorenko) if the random tournament asymptotically minimizes…
The celebrated K\H{o}v\'ari-S\'os-Tur\'an theorem states that any $n$-vertex graph containing no copy of the complete bipartite graph $K_{s,s}$ has at most $O_s(n^{2-1/s})$ edges. In the past two decades, motivated by the applications in…
In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs…