相关论文: Parallel edges in ribbon graphs and interpolating …
PED partitions are partitions with even parts distinct while odd parts are unrestricted. Similarly, POD partitions have distinct odd parts while even parts are unrestricted. Merca proved several recurrence relations analytically for the…
Given a planar graph $G$ and a partition of the neighbors of each vertex $v$ in four sets $UR(v)$, $UL(v)$, $DL(v)$, and $DR(v)$, the problem Windrose Planarity asks to decide whether $G$ admits a windrose-planar drawing, that is, a planar…
A \emph{proportionally dense subgraph} (PDS) is an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the rest of the graph. In this paper, we study…
An induced matching in a graph $G$ is a matching such that its end vertices also induce a matching. A $(1^{\ell}, 2^k)$-packing edge-coloring of a graph $G$ is a partition of its edge set into disjoint unions of $\ell$ matchings and $k$…
It is shown that every complete n-vertex simple topological graph has at least Omega(n^{1/3}) pairwise disjoint edges, and these edges can be found in polynomial time. This proves a conjecture of Pach and T\'oth.
An $r$-regular graph is an $r$-graph, if every odd set of vertices is connected to its complement by at least $r$ edges. Seymour [On multicolourings of cubic graphs, and conjectures of Fulkerson and Tutte.~\emph{Proc.~London…
A theorem of Cohn and Lempel [J. Combin. Theory Ser. A 13 (1972), 83-89] gives an equality relating the number of circuits in a directed circuit partition of a 2-in, 2-out digraph to the GF(2)-nullity of an associated matrix. This equality…
The Unfriendly Partition Problem asks whether it is possible to split the vertex set of an infinite graph $G$ into two parts so that every vertex has at least as many neighbors in the other part than on its own. Despite the uncountable…
Usually, mathematical objects have highly parallel interpretations. In this paper, we consider them as sequential constructors of other objects. In particular, we prove that every reflexive directed graph can be interpreted as a program…
We prove that any \(2\)-connected graph \(G\) on \(n\) vertices with minimum degree \(\delta(G) \ge \frac{n}{4}+2\) contains a \(2\)-connected subgraph of order \(k\) for every integer \(k\) with \(4 \le k \le n\). This improves a previous…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
Many important problems in extremal combinatorics can be stated as certifying polynomial inequalities in graph homomorphism numbers, and in particular, many ask to certify pure binomial inequalities. For a fixed collection of graphs…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel). Not all directed graphs contain kernels, and computing a kernel or deciding…
For a ribbon graph $G$, let $\gamma(G)$ denote its Euler genus. Recently, Chen, Gross and Tucker [J. Algebraic Combin. 63 (2026) 13] derived a formula for the maximum partial-dual Euler-genus $\partial\gamma_M(G)$ of a ribbon graph $G$.…
Traditional representations of graphs and their duals suggest the requirement that the dual vertices be placed inside their corresponding primal faces, and the edges of the dual graph cross only their corresponding primal edges. We consider…
We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover, we introduce a new switching of graphs which does not change some algebraic invariants of graphs, and using this, we study the linear strand of the…
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable ``interlace polynomial'' for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and…
A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. Resolving a recent question of Bennett, Dudek, and…
In a generalized Tur\'an problem, two graphs $H$ and $F$ are given and the question is the maximum number of copies of $H$ in an $F$-free graph of order $n$. In this paper, we study the number of double stars $S_{k,l}$ in triangle-free…