{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T18:10:51Z","timestamp":1648577451013},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"ELKH Alfr\u00e9d R\u00e9nyi Institute of Mathematics"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2021,12]]},"abstract":"Abstract<\/jats:title>For a given integer $$k\\ge 1$$<\/jats:tex-math>\n \n k<\/mml:mi>\n \u2265<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a graph G<\/jats:italic> with at least 2k<\/jats:italic> vertices is called k<\/jats:italic>-path-pairable, if for any set of k<\/jats:italic> disjoint pairs of vertices, $$s_i,t_i$$<\/jats:tex-math>\n \n \n s<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n ,<\/mml:mo>\n \n t<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, $$1\\le i\\le k$$<\/jats:tex-math>\n \n 1<\/mml:mn>\n \u2264<\/mml:mo>\n i<\/mml:mi>\n \u2264<\/mml:mo>\n k<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, there exist pairwise edge-disjoint $$s_i,t_i$$<\/jats:tex-math>\n \n \n s<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n ,<\/mml:mo>\n \n t<\/mml:mi>\n i<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-paths in G<\/jats:italic>. The path-pairability numberis the largest k<\/jats:italic> such that G<\/jats:italic> is k<\/jats:italic>-path-pairable. Bounds on the path-pairability number are given here if G<\/jats:italic> is the graph of infinite integer grids in the Euclidean plane. We prove that the path-pairability number of the integer quadrant is 4, and we show that the integer half-plane is 6-path-pairable and at most 7-path-pairable.\n<\/jats:p>","DOI":"10.1007\/s10998-021-00381-2","type":"journal-article","created":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T09:04:25Z","timestamp":1621587865000},"page":"220-232","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Path-pairability of infinite planar grids"],"prefix":"10.1007","volume":"83","author":[{"given":"Adam S.","family":"Jobson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9 E.","family":"K\u00e9zdy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jen\u0151","family":"Lehel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"key":"381_CR1","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s00453-003-1023-8","volume":"36","author":"W-T Chan","year":"2003","unstructured":"W.-T. 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Soc."},{"key":"381_CR5","unstructured":"C-C. Hsu, A genetic algorithm for maximum edge-disjoint paths problem and its extension to routing and wavelength assignment problem. Ph.D. thesis, North Carolina State University, 2013"},{"key":"381_CR6","doi-asserted-by":"publisher","first-page":"1352","DOI":"10.1007\/s40879-018-0306-1","volume":"5","author":"AS Jobson","year":"2019","unstructured":"A.S. Jobson, A.E. K\u00e9zdy, J. Lehel, On path-pairability of the finite grids. Eur. J. Math. 5, 1352\u20131363 (2019)","journal-title":"Eur. J. Math."},{"key":"381_CR7","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.ipl.2018.05.001","volume":"137","author":"AS Jobson","year":"2018","unstructured":"A.S. Jobson, A.E. K\u00e9zdy, J. Lehel, Linkage on the infinite grid. Inf. Process. Lett. 137, 51\u201356 (2018)","journal-title":"Inf. Process. Lett."},{"key":"381_CR8","unstructured":"A.S. Jobson, A.E. K\u00e9zdy, J. Lehel, The $$6\\times 6$$ grid is $$4$$-path-pairable. 2017. arXiv:1708.05407"},{"key":"381_CR9","unstructured":"A.S. Jobson, A.E. K\u00e9zdy, J. Lehel, Escaping from the corner of a grid by edge-disjoint paths. 2017. arXiv:1708.05413"},{"key":"381_CR10","doi-asserted-by":"publisher","first-page":"909","DOI":"10.7151\/dmgt.2114","volume":"39","author":"AS Jobson","year":"2019","unstructured":"A.S. Jobson, A.E. K\u00e9zdy, J. Lehel, G. M\u00e9sz\u00e1ros, The path-pairability number of products of stars. Discuss. Math. Graph Theory 39, 909\u2013924 (2019)","journal-title":"Discuss. Math. Graph Theory"},{"key":"381_CR11","doi-asserted-by":"publisher","first-page":"743","DOI":"10.7151\/dmgt.1888","volume":"36","author":"G M\u00e9sz\u00e1ros","year":"2016","unstructured":"G. M\u00e9sz\u00e1ros, On path-pairability in the Cartesian product of graphs. Discuss. Math. Graph Theory 36, 743\u2013758 (2016)","journal-title":"Discuss. Math. Graph Theory"},{"key":"381_CR12","doi-asserted-by":"crossref","unstructured":"G. M\u00e9sz\u00e1ros, Linkedness and path-pairability in the Cartesian product of graphs. 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