{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:36:38Z","timestamp":1759638998175},"reference-count":12,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5062,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a multigraph of maximum degree \u0394 and with a set of <jats:italic>t<\/jats:italic> vertices of degree one, called terminals. We call <jats:italic>G<\/jats:italic> a (\u0394, <jats:italic>t<\/jats:italic>)\u2010<jats:italic>network<\/jats:italic> if for any pairing of its terminals there exist edge\u2010disjoint paths in <jats:italic>G<\/jats:italic> between those pairs (<jats:italic>t<\/jats:italic> is even). The concept of (\u0394, <jats:italic>t<\/jats:italic>)\u2010networks is introduced to model the situation when switching processors having \u0394 ports are to be connected in such a way that simultaneous communication is possible for any pairing of the free ports. We establish some properties of (\u0394, <jats:italic>t<\/jats:italic>)\u2010<jats:italic>networks<\/jats:italic>. In particular, we investigate optimal (or near\u2010optimal) networks and obtain lower and upper bounds on the function <jats:italic>n<\/jats:italic>(\u0394, <jats:italic>t<\/jats:italic>), the minimum number of interior nodes a (\u0394, <jats:italic>t<\/jats:italic>)\u2010<jats:italic>network<\/jats:italic> can have.<\/jats:p>","DOI":"10.1002\/net.3230220702","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T13:17:06Z","timestamp":1178975826000},"page":"615-626","source":"Crossref","is-referenced-by-count":15,"title":["Networks communicating for each pairing of terminals"],"prefix":"10.1002","volume":"22","author":[{"given":"L\u00e1szl\u00f3","family":"Csaba","sequence":"first","affiliation":[]},{"given":"Ralph J.","family":"Faudree","sequence":"additional","affiliation":[]},{"given":"Andr\u00e1s","family":"Gy\u00e1rf\u00e1s","sequence":"additional","affiliation":[]},{"given":"Jen\u00f6","family":"Lehel","sequence":"additional","affiliation":[]},{"given":"Richard H.","family":"Schelp","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_3_2","unstructured":"R. J.Faudree A.Gy\u00e1rf\u00e1s andJ.Lehel Minimal path pairable graphs. Manuscript in preparation."},{"key":"e_1_2_1_4_2","unstructured":"R. J.Faudree A.Gy\u00e1rf\u00e1s andJ.Lehel Three\u2010regular path pairable graphs.Graphs Combinatorics to appear."},{"key":"e_1_2_1_5_2","first-page":"47","volume-title":"Paths, Flows, and VLSI\u2010Loyout","author":"Frank A.","year":"1990"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01787639"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01350174"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-20.1.144"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90040-1"},{"key":"e_1_2_1_10_2","first-page":"3","volume-title":"Graph\u2010Theoretic Concepts in Computer Science","author":"Madhavapeddy S."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392606"},{"key":"e_1_2_1_12_2","first-page":"329","volume-title":"Paths, Flows, and VLSI\u2010Layout","author":"Schrijver A.","year":"1990"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1949281148"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230220702","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230220702","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T09:39:59Z","timestamp":1698053999000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230220702"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,12]]},"references-count":12,"journal-issue":{"issue":"7","published-print":{"date-parts":[[1992,12]]}},"alternative-id":["10.1002\/net.3230220702"],"URL":"https:\/\/doi.org\/10.1002\/net.3230220702","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,12]]}}}