On properties of maximal 1-planar graphs
نویسندگان
چکیده
A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.
منابع مشابه
Testing Maximal 1-Planarity of Graphs with a Rotation System in Linear Time - (Extended Abstract)
A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. A 1-planar graph on n vertices can have at most 4n− 8 edges. It is known that testing 1-planarity of a graph is NP-complete. A 1-planar embedding of a graph G is maximal, if no edge can be added without violating the 1-planarity of G. In this paper, we study combinatorial properties of maximal 1-pl...
متن کاملOn topological aspects of orientations
1. Introduction Constrained orientations, that is orientations such that all the vertices have a prescribed indegree, relates to one another many combinatorial and topological properties such as arboricity, connectivity and planarity. These orientations are the basic tool to solve planar augmentation problems 2]. We are concerned with two classes of planar graphs: maximal planar graphs (i.e. po...
متن کاملSome Results on the Maximal 2-Rainbow Domination Number in Graphs
A 2-rainbow dominating function ( ) of a graph is a function from the vertex set to the set of all subsets of the set such that for any vertex with the condition is fulfilled, where is the open neighborhood of . A maximal 2-rainbow dominating function on a graph is a 2-rainbow dominating function such that the set is not a dominating set of . The weight of a maximal is the value . ...
متن کاملOn the M-polynomial of planar chemical graphs
Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices...
متن کاملAn update on non-Hamiltonian 54-tough maximal planar graphs
Studying the shortness of longest cycles in maximal planar graphs, we improve the upper bound on the shortness exponent of the class of 54 -tough maximal planar graphs presented by Harant and Owens [Discrete Math. 147 (1995), 301–305]. In addition, we present two generalizations of a similar result of Tkáč who considered 1-tough maximal planar graphs [Discrete Math. 154 (1996), 321–328]; we rem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 32 شماره
صفحات -
تاریخ انتشار 2012