{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T06:59:42Z","timestamp":1649141982369},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> Given a tree T, a configuration of T is denoted by [Formula: see text] which represents that there is a robot at the vertex u, a hole at the vertex v and obstacles in the remaining vertices of T. By an mRJ move we mean that the robot is moved from the vertex u to a vertex v having a hole by jumping over m obstacles along a path. The case m = 0 is a simple move of taking the robot from u to the adjacent vertex v with a hole. We investigate the problem of moving a robot from its initial position to all the other vertices using mRJ moves (for some fixed m) in addition to simple moves. A tree is said to be mRJ reachable if there exists a configuration from which it is possible to take the robot to any vertex of the tree using simple or mRJ moves. A connected graph is 1RJ reachable. However, for m \u2265 2 there exists graphs that are not mRJ reachable. We characterize 2RJ and 3RJ reachable trees and give bound for the diameter of mRJ reachable trees. <\/jats:p>","DOI":"10.1142\/s1793830912500553","type":"journal-article","created":{"date-parts":[[2012,9,25]],"date-time":"2012-09-25T15:17:45Z","timestamp":1348586265000},"page":"1250055","source":"Crossref","is-referenced-by-count":2,"title":["ON <i>mRJ<\/i> REACHABILITY IN TREES"],"prefix":"10.1142","volume":"04","author":[{"given":"BISWAJIT","family":"DEB","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India"}]},{"given":"KALPESH","family":"KAPOOR","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India"}]},{"given":"SUKANTA","family":"PATI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India"}]}],"member":"219","published-online":{"date-parts":[[2013,1,4]]},"reference":[{"key":"rf2","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2005.01.018"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(86)90146-5"},{"key":"rf5","unstructured":"C. H.\u00a0Papadimitriou, Foundations of Computer Science (1994)\u00a0pp. 511\u2013520."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80001-6"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2010.02.001"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500553","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:14:28Z","timestamp":1565111668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":6,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,1,4]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S1793830912500553"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500553","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}