{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:09:23Z","timestamp":1761620963206},"reference-count":61,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7337,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1986,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An overview of Eulerian graphs is presented. In particular, characterizations of Eulerian graphs and digraphs as well as algorithms for constructing Eulerian circuits are discussed. A solution to the Chinese postman problem is followed by a study of subgraphs and supergraphs of Eulerian graphs. After an introduction to randomly Eulerian graphs and digraphs, we conclude with a summary of a variety of results involving enumeration.<\/jats:p>","DOI":"10.1002\/jgt.3190100306","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:54:31Z","timestamp":1180180471000},"page":"277-297","source":"Crossref","is-referenced-by-count":20,"title":["An Eulerian exposition"],"prefix":"10.1002","volume":"10","author":[{"given":"Linda","family":"Lesniak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ortrud R.","family":"Oellermann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"203","article-title":"Circuits and trees in oriented linear graphs","volume":"28","author":"van Aardenne\u2010Ehrenfest T.","year":"1951","journal-title":"Simon Stevin"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02564555"},{"key":"e_1_2_1_4_2","volume-title":"Graphs and Digraphs","author":"Behzad M.","year":"1981"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90048-1"},{"key":"e_1_2_1_6_2","first-page":"193","article-title":"On the number of balanced orientations of even graphs","volume":"23","author":"Berman K. A.","year":"1979","journal-title":"Congressus Numerantium"},{"key":"e_1_2_1_7_2","volume-title":"Graph Theory 1736\u20131936","author":"Biggs N. L.","year":"1976"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010115"},{"key":"e_1_2_1_9_2","article-title":"Parity theorems for paths and cycles in graphs","author":"Bondy J. A.","journal-title":"J. Graph Theory"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","first-page":"424","DOI":"10.21136\/CMJ.1971.101043","article-title":"Randomly eulerian digraphs","volume":"21","author":"Chartrand G.","year":"1971","journal-title":"Czech. Math. J."},{"key":"e_1_2_1_11_2","first-page":"101","article-title":"Randomly traversable graphs","volume":"25","author":"Chartrand G.","year":"1970","journal-title":"Elem. Math."},{"key":"e_1_2_1_12_2","first-page":"47","article-title":"Eulerian trails with prescribed degrees in tournaments","volume":"12","author":"Das P.","year":"1981","journal-title":"Ars Combin."},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","first-page":"319","DOI":"10.7146\/math.scand.a-11439","article-title":"On arbitrarily traceable graphs","volume":"31","author":"Dirac G.","year":"1972","journal-title":"Math. Scand."},{"issue":"1","key":"e_1_2_1_14_2","first-page":"B73","article-title":"The Chinese postman problem","volume":"13","author":"Edmonds J.","year":"1965","journal-title":"Oper. Res."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.013"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580113"},{"key":"e_1_2_1_17_2","first-page":"128","article-title":"Solutio problematis ad geometriam situs pertinentis","volume":"8","author":"Euler L.","year":"1736","journal-title":"Comment. Acad. Sci. Petropolitanae"},{"key":"e_1_2_1_18_2","first-page":"17","volume-title":"Selected Topics in Graph Theory 2","author":"Fleischner H.","year":"1983"},{"key":"e_1_2_1_19_2","first-page":"177","article-title":"A way of enumerating Eulerian trails in a connected Eulerian graph","volume":"16","author":"Fleischner H.","year":"1983","journal-title":"Ars. Combin."},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1137\/0202003"},{"key":"e_1_2_1_21_2","unstructured":"I. S.GrunskiiandD. V.Speranskii The length of a round of a graph.Kibernetika (Kiev)(1973)34\u201337."},{"key":"e_1_2_1_22_2","first-page":"263","article-title":"Graphic programming using odd or even points","volume":"10","author":"Guan M.","year":"1960","journal-title":"Acta Math. Sinica"},{"key":"e_1_2_1_22_3","first-page":"273","volume":"1","year":"1962","journal-title":"Chinese Math."},{"key":"e_1_2_1_23_2","first-page":"37","article-title":"On arbitrarily traceable graphs and directed graphs","volume":"23","author":"Harary F.","year":"1957","journal-title":"Scripta Math."},{"key":"e_1_2_1_24_2","volume-title":"Graphical Enumeration","author":"Harary F.","year":"1973"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010208"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01442866"},{"key":"e_1_2_1_27_2","unstructured":"F.Jaeger On nowhere\u2010zero flows in multigraphs.Proc. 5th British Combin. Conf.(1975)373\u2013378."},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190030110"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(79)90057-1"},{"key":"e_1_2_1_30_2","first-page":"111","article-title":"Hypo\u2010eulerian and hypo\u2010traversable graphs","volume":"28","author":"Kapoor S. F.","year":"1973","journal-title":"Elem. Math."},{"key":"e_1_2_1_31_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-95-3-189-194"},{"key":"e_1_2_1_32_2","first-page":"14","article-title":"On directed postman problems","volume":"8","author":"Koh K. M.","year":"1974","journal-title":"Nanta Math. Part III"},{"key":"e_1_2_1_33_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010412"},{"key":"e_1_2_1_34_2","first-page":"31","article-title":"\u00dcber die im gleichgewicht gerichteten endlichen graphen","volume":"84","author":"Kotzig A.","year":"1959","journal-title":"\u010casopis P\u011bst. Mat."},{"key":"e_1_2_1_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90087-2"},{"key":"e_1_2_1_36_2","first-page":"193","article-title":"Degree sets and traversability","volume":"10","author":"Lesniak L.","year":"1978","journal-title":"Rend. Mat."},{"key":"e_1_2_1_37_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1977-034-8"},{"key":"e_1_2_1_38_2","unstructured":"V. A.Liskovec The number of Eulerian digraphs and homogeneous tournaments.Vesci Adad. Nauk BSSR Ser. Fiz.\u2010Mat.(Russian) (1971)22\u201327."},{"key":"e_1_2_1_39_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062534"},{"key":"e_1_2_1_40_2","unstructured":"E.Lucas R\u00e9cr\u00e9ations Math\u00e9matiques IV Paris(1921)."},{"key":"e_1_2_1_41_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020207"},{"key":"e_1_2_1_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90004-9"},{"key":"e_1_2_1_43_2","doi-asserted-by":"publisher","DOI":"10.1017\/S000497270001114X"},{"key":"e_1_2_1_44_2","first-page":"107","article-title":"A theorem on hamiltonian line graphs","volume":"14","author":"Nebesk\u00fd L.","year":"1973","journal-title":"Comment. Math. Univ. Carolin."},{"key":"e_1_2_1_45_2","doi-asserted-by":"crossref","first-page":"298","DOI":"10.21136\/CMJ.1979.101606","article-title":"On Eulerian subgraphs of complementary graphs","volume":"29","author":"Nebesk\u00fd L.","year":"1979","journal-title":"Czech. Math. J."},{"key":"e_1_2_1_46_2","first-page":"183","article-title":"Graphs for which all strong orientations are Eulerian","volume":"2","author":"Oellermann O. R.","year":"1984","journal-title":"Exposition. Math."},{"key":"e_1_2_1_47_2","first-page":"49","article-title":"A problem regarding the tracing of graphs","volume":"6","author":"Ore O.","year":"1951","journal-title":"Elem. Math."},{"key":"e_1_2_1_48_2","first-page":"385","volume-title":"Selected Topics in Graph Theory 1","author":"Palmer E. M.","year":"1978"},{"key":"e_1_2_1_49_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1962-039-0"},{"key":"e_1_2_1_50_2","unstructured":"R. J.Riddell Contributions to the Theory of Condensation. Ph.D. thesis University of Michigan Ann Arbor (1951)."},{"key":"e_1_2_1_51_2","first-page":"147","volume-title":"Proof Techniques in Graph Theory","author":"Robinson R. W.","year":"1969"},{"key":"e_1_2_1_52_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(81)90034-4"},{"key":"e_1_2_1_53_2","first-page":"107","article-title":"Some parity results on binary vector spaces","volume":"8","author":"Shank H.","year":"1979","journal-title":"Ars Combin."},{"key":"e_1_2_1_54_2","unstructured":"V. S.\u0160i\u0161ovandHo BaThuan Remark on Tarri\u015b method of counting Euler cycles.Kibernetika (Kiev)(1968)76\u201380."},{"key":"e_1_2_1_55_2","first-page":"191","article-title":"A formula for the number of Euler cycles of a complete graph Un","volume":"24","author":"Sorokin V. A.","year":"1969","journal-title":"Uspehi Mat. Nauk"},{"key":"e_1_2_1_56_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(72)90046-9"},{"key":"e_1_2_1_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(73)90046-X"},{"key":"e_1_2_1_58_2","doi-asserted-by":"publisher","DOI":"10.2307\/2302716"},{"key":"e_1_2_1_59_2","doi-asserted-by":"publisher","DOI":"10.2307\/1967604"},{"key":"e_1_2_1_60_2","unstructured":"V. G.VizingandM. K.Goldberg The length of a circuit of a strongly connected graph.Kibernetika (Kiev)(1969)79\u201382."},{"key":"e_1_2_1_61_2","doi-asserted-by":"crossref","first-page":"564","DOI":"10.21136\/CMJ.1979.101637","article-title":"Some remarks on Eulerian graphs","volume":"29","author":"Zelinka B.","year":"1979","journal-title":"Czech. Math. J."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190100306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190100306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T18:46:06Z","timestamp":1697913966000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190100306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,9]]},"references-count":61,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1986,9]]}},"alternative-id":["10.1002\/jgt.3190100306"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190100306","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,9]]}}}