相关论文: Well-quasi-ordering digraphs with no long alternat…

We consider the problem of decomposing the edges of a directed graph into as few paths as possible. There is a natural lower bound for the number of paths needed in an edge decomposition of a directed graph $D$ in terms of its degree…

We study the detection and the reconstruction of a large very dense subgraph in a social graph with $n$ nodes and $m$ edges given as a stream of edges, when the graph follows a power law degree distribution, in the regime when $m=O(n. \log…

The well-quasi-orders (WQO) play an important role in various fields such as Computer Science, Logic or Graph Theory. Since the class of WQOs lacks closure under some important operations, the proof that a certain quasi-order is WQO…

We prove that every graph $G$ on $n$ vertices with no isolated vertices contains an induced subgraph of size at least $n/10000$ with all degrees odd. This solves an old and well-known conjecture in graph theory.

We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree…

We attempt to generalize a theorem of Nash-Williams stating that a graph has a $k$-arc-connected orientation if and only if it is $2k$-edge-connected. In a strongly connected digraph we call an arc {\it deletable} if its deletion leaves a…

In a seminal work, K\"uhn, Osthus, Townsend, and Zhao used the hypergraph container method to determine the typical structure of oriented graphs and digraphs avoiding a fixed tournament or cycle. Their main tool, a container theorem for…

While the theory of labelled well-quasi-order has received significant attention in the graph setting, it has not yet been considered in the context of permutation patterns. We initiate this study here, and show how labelled well quasi…

A graph $H$ is an induced minor of a graph $G$ if it can be obtained from an induced subgraph of $G$ by contracting edges. Otherwise, $G$ is said to be $H$-induced minor-free. Robin Thomas showed that $K_4$-induced minor-free graphs are…

A graph H is strongly immersed in G if G is obtained from H by a sequence of vertex splittings (i.e., lifting some pairs of incident edges and removing the vertex) and edge removals. Equivalently, vertices of H are mapped to distinct…

A graph $G$ contains $H$ as an \emph{immersion} if there is an injective mapping $\phi: V(H)\rightarrow V(G)$ such that for each edge $uv\in E(H)$, there is a path $P_{uv}$ in $G$ joining vertices $\phi(u)$ and $\phi(v)$, and all the paths…

Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…

This paper is the first from a series of papers that establish a common analogue of the strong component and basilica decompositions for bidirected graphs. A bidirected graph is a graph in which a sign $+$ or $-$ is assigned to each end of…

We establish mild conditions under which a possibly irregular, sparse graph $G$ has "many" strong orientations. Given a graph $G$ on $n$ vertices, orient each edge in either direction with probability $1/2$ independently. We show that if…

We show that for every $\eta>0$ every sufficiently large $n$-vertex oriented graph D of minimum semidegree exceeding $(1 + \eta) k/2$ contains every balanced antidirected tree with $k$ edges and bounded maximum degree, if $k \ge \eta n$. In…

This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse…

The general position number for graphs ask for largest vertex subsets $S$ such that no three vertices are contained on a common shortest path. We examine this problem in the setting of directed graphs. We provide bounds for the general…

Daligault, Rao and Thomass\'e asked whether every hereditary graph class that is well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev (JCTB 2017+) gave a negative answer to this question,…

An infinite graph is said to be highly connected if the induced subgraph on the complement of any set of vertices of smaller size is connected. We continue the study of weaker versions of Ramsey Theorem on uncountable cardinals asserting…

The concept of antimagic labelings of a graph is to produce distinct vertex sums by labeling edges through consecutive numbers starting from one. A long-standing conjecture is that every connected graph, except a single edge, is antimagic.…