Related papers: Matching Book Embedding of the Cartesian Product o…
We study linkedness of Cartesian product of graphs and prove that the product of an $a$-linked and a $b$-linked graphs is $(a+b-1)$-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine…
In 1999, Heath, Pemmaraju, and Trenk [SIAM J. Comput. 28(4), 1999] extended the classic notion of book embeddings to digraphs, introducing the concept of upward book embeddings, in which the vertices must appear along the spine in a…
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect…
The enumeration of perfect matchings of graphs is equivalent to the dimer problem which has applications in statistical physics. A graph $G$ is said to be $n$-rotation symmetric if the cyclic group of order $n$ is a subgroup of the…
Image feature matching is a fundamental part of many geometric computer vision applications, and using multiple images can improve performance. In this work, we formulate multi-image matching as a graph embedding problem then use a Graph…
Given a graph $G$ with a total order defined on its vertices, the Maximum Pagenumber-$k$ Subgraph Problem asks for a maximum subgraph $G'$ of $G$ such that $G'$ can be embedded into a $k$-book when the vertices are placed on the spine…
The thickness $\theta(G)$ of a graph $G$ is the minimum number of planar spanning subgraphs into which the graph $G$ can be decomposed. It is a topological invariant of a graph, which was defined by W.T. Tutte in 1963 and also has important…
We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of $K_n\times G$ is found, provided that $G$…
In a book embedding the vertices of a graph are placed on the "spine" of a "book" and the edges are assigned to "pages" so that edges on the same page do not cross. In the Partitioned 2-page Book Embedding problem egdes are partitioned into…
A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recently, Biedl and Wittnebel proved that every 1-planar graph…
A connected graph $G$, of order two or more, is matching covered if each edge lies in some \pema. The tight cut decomposition of a matching covered graph $G$ yields a list of bricks and braces; as per a theorem of Lov{\'a}sz~\cite{lova87},…
A leaf matching operation on a graph consists of removing a vertex of degree~$1$ together with its neighbour from the graph. For $k\geq 0$, let $G$ be a $d$-regular cyclically $(d-1+2k)$-edge-connected graph of even order. We prove that for…
We obtain a criterion for approximability by embeddings of piecewise linear maps of a circle to the plane, analogous to the one proved by Minc for maps of a segment to the plane. Theorem. Let S be a triangulation of a circle with s…
In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art…
Knowledge Graph embedding provides a versatile technique for representing knowledge. These techniques can be used in a variety of applications such as completion of knowledge graph to predict missing information, recommender systems,…
A "book with k pages" consists of a straight line (the "spine") and k half-planes (the "pages"), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine,…
Knowledge Graph Completion is a task of expanding the knowledge graph/base through estimating possible entities, or proper nouns, that can be connected using a set of predefined relations, or verb/predicates describing interconnections of…
We introduce and study a generalization of conformal rigidity for graphs. A graph is $k$-conformally rigid if the uniform edge weights simultaneously maximize the sum of the $k$ smallest nontrivial Laplacian eigenvalues and minimize the sum…
A matching is a set of edges without common endpoint. It was recently shown that every 1-planar graph (i.e., a graph that can be drawn in the plane with at most one crossing per edge) that has minimum degree 3 has a matching of size at…
A book embedding of the complete graph $K_n$ needs $\lceil \frac{n}{2} \rceil$ pages and the page-subgraphs can be chosen to be spanning paths (for $n$ even) and one spanning star for $n$ odd. We show that all page-subgraphs can be chosen…