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Paper Abstract and Keywords
Presentation 2018-03-05 14:50
A recognition algorithm for simple-triangle graphs
Asahi Takaoka (Kanagawa Univ.) COMP2017-50
Abstract (in Japanese) (See Japanese page) 
(in English) A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a longstanding open problem, which was recently settled. This paper provides a new recognition algorithm for simple-triangle graphs to improve the time bound from $O(n^2 overline{m})$ to $O(nm)$, where $n$, $m$, and $overline{m}$ are the number of vertices, edges, and non-edges of the graph, respectively. The algorithm uses the vertex ordering characterization in our previous paper that a graph is a simple-triangle graph if and only if there is a linear ordering of the vertices containing both an alternating orientation of the graph and a transitive orientation of the complement of the graph. We also show, as a byproduct, that an alternating orientation can be obtained in $O(nm)$ time for cocomparability graphs, and it is NP-complete to decide whether a cocomparability graph has an orientation that is alternating and acyclic.
Keyword (in Japanese) (See Japanese page) 
(in English) Alternately orientable graphs / Cocomparability graphs / Intersection graphs / PI graphs / Recognition algorithm / Simple-triangle graphs / Vertex ordering characterization /  
Reference Info. IEICE Tech. Rep., vol. 117, no. 474, COMP2017-50, pp. 27-34, March 2018.
Paper # COMP2017-50 
Date of Issue 2018-02-26 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2017-50

Conference Information
Committee COMP  
Conference Date 2018-03-05 - 2018-03-05 
Place (in Japanese) (See Japanese page) 
Place (in English) Osaka Prefecture Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2018-03-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A recognition algorithm for simple-triangle graphs 
Sub Title (in English)  
Keyword(1) Alternately orientable graphs  
Keyword(2) Cocomparability graphs  
Keyword(3) Intersection graphs  
Keyword(4) PI graphs  
Keyword(5) Recognition algorithm  
Keyword(6) Simple-triangle graphs  
Keyword(7) Vertex ordering characterization  
Keyword(8)  
1st Author's Name Asahi Takaoka  
1st Author's Affiliation Kanagawa University (Kanagawa Univ.)
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Speaker Author-1 
Date Time 2018-03-05 14:50:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # COMP2017-50 
Volume (vol) vol.117 
Number (no) no.474 
Page pp.27-34 
#Pages 8 
Date of Issue 2018-02-26 (COMP) 

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