Drawing Graphs Using a Small Number of Obstacles
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313926" target="_blank" >RIV/00216208:11320/15:10313926 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007/978-3-319-27261-0_30" target="_blank" >http://link.springer.com/chapter/10.1007/978-3-319-27261-0_30</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-27261-0_30" target="_blank" >10.1007/978-3-319-27261-0_30</a>
Alternative languages
Result language
angličtina
Original language name
Drawing Graphs Using a Small Number of Obstacles
Original language description
An obstacle representation of a graph G is a set of points in the plane representing the vertices of G, together with a set of polygonal obstacles such that two vertices of G are connected by an edge in G if and only if the line segment between the corresponding points avoids all the obstacles. The obstacle number obs(G) of G is the minimum number of obstacles in an obstacle representation of G. We provide the first non-trivial general upper bound on the obstacle number of graphs by showing that every n-vertex graph G satisfies obs(G) LESS-THAN OR EQUAL TO 2nlogn. This refutes a conjecture of Mukkamala, Pach, and Pálvölgyi. For bipartite n-vertex graphs, we improve this bound to n MINUS SIGN 1. Both bounds apply even when the obstacles are required tobe convex. We also prove a lower bound 2?(hn) on the number of n-vertex graphs with obstacle number at most h for h < M and an asymptotically matching lower bound ?(n4/3M2/3) for the complexity of a collection of M GREATER-THAN OR EQUAL T
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Graph Drawing and Network Visualization
ISBN
978-3-319-27260-3
ISSN
0302-9743
e-ISSN
—
Number of pages
13
Pages from-to
360-372
Publisher name
Springer International Publishing
Place of publication
Neuveden
Event location
Los Angeles, CA, USA
Event date
Sep 24, 2015
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—