相关论文: Odd wheels are not odd-distance graphs
An oriented 3-graph consists of a family of triples (3-sets), each of which is given one of its two possible cyclic orientations. A cycle in an oriented 3-graph is a positive sum of some of the triples that gives weight zero to each 2-set.…
A thrackle is a graph drawing in which every pair of edges meets exactly once. The Thrackle Conjecture (established by John Conway) states that the number of edges of a thrackle cannot exceed the number of its vertices. Cairns, Koussas, and…
A graph is circle if its vertices are in correspondence with a family of chords in a circle in such a way that every two distinct vertices are adjacent if and only if the corresponding chords have nonempty intersection. Even though there…
In this paper we construct all strongly regular graphs, with at most 600 vertices, admitting a transitive action of the orthogonal group $O^+(6,2)$ or $O^-(6,2)$. Consequently, we prove the existence of strongly regular graphs with…
A wheel graph consists of a cycle along with a center vertex connected to every vertex in the cycle. In this paper we show that every subgraph of a wheel graph has list coupled chromatic number at most 5, and this coloring can be found in…
We prove that for any given $\varepsilon>0$ and $d\in [0,1]$, every sufficiently large $(\varepsilon, d)$-dense graph $G$ contains for each odd integer $r$ at least $(d^r-\varepsilon)|V(G)|^r$ cycles of length $r$. Here, $G$ being…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
We show that every quadrangulation of the sphere can be transformed into a $4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident edges at a…
Low density graphs are considered to be a realistic graph class for modelling road networks. It has advantages over other popular graph classes for road networks, such as planar graphs, bounded highway dimension graphs, and spanners. We…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
One must add arrows which are forced by transitivity to form the transitive closure of a directed graph. We introduce a construction of a transitive directed graph which is formed by adding vertices instead of arrows and which preserves the…
A nut graph is a nontrivial graph whose adjacency matrix has a one-dimensional null space spanned by a vector without zero entries. Recently, it was shown that a nut graph has more edge orbits than vertex orbits. It was also shown that for…
A graph is said to be globally rigid if almost all embeddings of the graph's vertices in the Euclidean plane will define a system of edge-length equations with a unique (up to isometry) solution. In 2007, Jackson, Servatius and Servatius…
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a special kind of simple drawings that we call generalized…
We study the structure of graphs that do not contain the wheel on 5 vertices W4 as an immersion, and show that these graphs can be constructed via 1, 2, and 3-edge-sums from subcubic graphs and graphs of bounded treewidth.
The transmission of a vertex $v$ of a graph $G$ is the sum of distances from $v$ to all the other vertices in $G$. A graph is transmission irregular if all of its vertices have pairwise different transmissions. A starlike tree…
The diameter of a graph is the maximum distance among all pairs of vertices. Thus a graph $G$ has diameter $d$ if any two vertices are at distance at most $d$ and there are two vertices at distance $d$. We are interested in studying the…
A hole in a graph G is an induced cycle of length at least four; an antihole is a hole in the complement of G. In 2005, Chudnovsky, Cornuejols, Liu, Seymour and Vuskovic showed that it is possible to test in polynomial time whether a graph…
Given an oriented graph $\overrightarrow{G}$ and $D$ a distance set of $\overrightarrow{G}$, $\overrightarrow{G}$ is $D$-antimagic if there exists a bijective vertex labeling such that the sum of all labels of the $D$-out-neighbors of each…
We prove that the class of 3D-grids is cannot be transduced from planar graphs, and more generally, from any class of graphs of bounded Euler genus. To prove our result, we introduce a new structural tool called slice decompositions, and…