Publication

On the Structure of Graphs with Low Obstacle Number

2011
Conference Papers

Abstract

The obstacle number of a graph G is the smallest number of polygonal obstacles in the plane with the property that the vertices of G can be represented by distinct points such that two of them see each other if and only if the corresponding vertices are joined by an edge. We list three small graphs that require more than one obstacle. Using extremal graph theoretic tools developed by Promel, Steger, Bollobas, Thomason, and others, we deduce that for any fixed integer h, the total number of graphs on n vertices with obstacle number at most h is at most 2(0(n2)). This implies that there are bipartite graphs with arbitrarily large obstacle number, which answers a question of Alpert et al. (Discret Comput Geom doi:10.1007/s00454-009-9233-8 Address="10.1007/s00454-009-9233-8" , 2009).

Official source

https://infoscience.epfl.ch/entities/publication/002b1693-cf04-41c1-91aa-1d6b79e9e429

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2011
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/002b1693-cf04-41c1-91aa-1d6b79e9e429

About this result

Related concepts (32)

Line graph

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.

Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.

Chordal graph

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree.

Related publications (18)

On the Structure of Graphs with Low Obstacle Number

Chat with Graph Search

Short monochromatic odd cycles

Tight bounds for intersection‐reverse sequences, edge‐ordered graphs, and applications

Tracing Ecological Metaphors in Discourses on Open Science using LLMs and Knowledge Graphs