{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T21:41:30Z","timestamp":1649194890314},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p>Let G be a 2-edge-connected undirected graph, A be an (additive) abelian group and A* = A-{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V(G) \u21a6 A satisfying \u03a3<jats:sub>\u03c5\u2208V(G)<\/jats:sub>b(\u03c5) = 0, there is a function f : E(G) \u21a6 A* such that for each vertex \u03c5 \u2208 V(G), the total amount of f values on the edges directed out from \u03c5 minus the total amount of f values on the edges directed into \u03c5 equals b(\u03c5). Let Z<jats:sub>3<\/jats:sub>denote the group of order 3. Jaeger et al. conjectured that there exists an integer k such that every k-edge-connected graph is Z<jats:sub>3<\/jats:sub>-connected. In this paper, we prove that every N<jats:sub>2<\/jats:sub>-locally connected claw-free graph G with minimum degree \u03b4(G) \u2265 7 is Z<jats:sub>3<\/jats:sub>-connected.<\/jats:p>","DOI":"10.1142\/s1793830911001140","type":"journal-article","created":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T13:20:39Z","timestamp":1310563239000},"page":"193-201","source":"Crossref","is-referenced-by-count":0,"title":["EVERY N<sub>2<\/sub>-LOCALLY CONNECTED CLAW-FREE GRAPH WITH MINIMUM DEGREE AT LEAST 7 IS Z<sub>3<\/sub>-CONNECTED"],"prefix":"10.1142","volume":"03","author":[{"given":"ERLING","family":"WEI","sequence":"first","affiliation":[{"name":"School of Information, Renming University of China, Beijing, P. R. China"}]},{"given":"YE","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA"}]},{"given":"PING","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA"}]},{"given":"HONG-JIAN","family":"LAI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA"},{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","volume-title":"Derived Graphs and Digraphs, Beitr\u00e4ge zur Graphentheorie","author":"Beineke L.","year":"1968"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2008.02.008"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/060677744"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.11.045"},{"key":"rf6","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"key":"rf7","unstructured":"F.\u00a0Jaeger, Selected Topics in Graph Theory, eds. 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