{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T16:16:45Z","timestamp":1774369005342,"version":"3.50.1"},"reference-count":45,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1973,5,1]],"date-time":"1973-05-01T00:00:00Z","timestamp":105062400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":14687,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Combinatorial Theory, Series A"],"published-print":{"date-parts":[[1973,5]]},"DOI":"10.1016\/0097-3165(73)90012-5","type":"journal-article","created":{"date-parts":[[2005,2,10]],"date-time":"2005-02-10T04:49:18Z","timestamp":1108010958000},"page":"364-385","source":"Crossref","is-referenced-by-count":75,"title":["Shortness exponents of families of graphs"],"prefix":"10.1016","volume":"14","author":[{"given":"Branko","family":"Gr\u00fcnbaum","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hansjoachim","family":"Walther","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0097-3165(73)90012-5_BIB1_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0012-365X(71)90011-2","article-title":"Polyhedral realizations in R3 of triangulations of the torus and 2-manifolds in cyclic 4-polytopes","volume":"1","author":"Altshuler","year":"1971","journal-title":"Discrete Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB1_2","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0012-365X(72)90037-4","article-title":"Hamiltonian circuits in some maps on the torus","volume":"1","author":"Altshuler","year":"1972","journal-title":"Discrete Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB2_1","doi-asserted-by":"crossref","first-page":"731","DOI":"10.4153\/CJM-1966-073-4","article-title":"Trees in polyhedral graphs","volume":"18","author":"Barnette","year":"1966","journal-title":"Canad. J. Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB2_2","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1007\/BF02771742","article-title":"A simple 4-dimensional nonfacet","volume":"7","author":"Barnette","year":"1969","journal-title":"Israel J. Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB3","series-title":"The Many Facets of Graph Theory","first-page":"27","article-title":"On Steinitz's theorem concerning convex 3-polytopes and on some properties of planar graphs","author":"Barnette","year":"1969"},{"key":"10.1016\/0097-3165(73)90012-5_BIB4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/S0021-9800(70)80054-0","article-title":"Hamiltonian circuits on 3-polytopes","volume":"9","author":"Barnette","year":"1970","journal-title":"J. Combinatorial Theory"},{"key":"10.1016\/0097-3165(73)90012-5_BIB5","series-title":"Graphes et hypergraphes","author":"Berge","year":"1970"},{"key":"10.1016\/0097-3165(73)90012-5_BIB6","series-title":"Proceedings of the International Symposium on the Theory of Graphs","first-page":"35","article-title":"Hamiltonian lines in cubic graphs","author":"Bos\u00e1k","year":"1967"},{"key":"10.1016\/0097-3165(73)90012-5_BIB7_1","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.2140\/pjm.1961.11.1211","article-title":"Simple paths on convex polyhedra","volume":"11","author":"Brown","year":"1961","journal-title":"Pacific J. Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB7_2","first-page":"53","article-title":"Maximal simple paths on convex polyhedra, Abstract 61T-1","volume":"8","author":"Brown","year":"1961","journal-title":"Notices Amer. Math. Soc."},{"key":"10.1016\/0097-3165(73)90012-5_BIB8_1","article-title":"Hamiltonian circuits on 3-dimensional, 3-valent, convex polytopes","author":"Butler","year":"1972"},{"key":"10.1016\/0097-3165(73)90012-5_BIB8_2","first-page":"A","volume":"19","author":"Butler","year":"1972","journal-title":"Notices Amer. Math. Soc."},{"key":"10.1016\/0097-3165(73)90012-5_BIB9","first-page":"69","article-title":"Some theorems on abstract graphs","volume":"2","author":"Dirac","year":"1952"},{"key":"10.1016\/0097-3165(73)90012-5_BIB10_1","article-title":"On shortness exponents of families of graphs","author":"Ewald","year":"1972","journal-title":"Israel J. Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB10_2","series-title":"Hamiltonian circuits on simplicial complexes","author":"Ewald","year":"1972"},{"key":"10.1016\/0097-3165(73)90012-5_BIB11","article-title":"Recursive generation of cyclically k-connected cubic planar graphs","author":"Faulkner","year":"1971"},{"key":"10.1016\/0097-3165(73)90012-5_BIB12","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0095-8956(72)90018-4","article-title":"Hamiltonian paths on 3-polytopes","volume":"12","author":"Goodey","year":"1972","journal-title":"J. Combinatorial Theory"},{"key":"10.1016\/0097-3165(73)90012-5_BIB13","first-page":"51","article-title":"Plane homogeneous graphs of degree three without Hamiltonian circuits (in Russian)","volume":"Vol. 4","author":"Grinberg","year":"1968"},{"key":"10.1016\/0097-3165(73)90012-5_BIB14_1","series-title":"Convex Polytopes","author":"Gr\u00fcnbaum","year":"1967"},{"key":"10.1016\/0097-3165(73)90012-5_BIB14_2","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1090\/S0002-9904-1970-12601-5","article-title":"Polytopes, graphs, and complexes","volume":"76","author":"Gr\u00fcnbaum","year":"1970","journal-title":"Bull. Amer. Math. Soc."},{"key":"10.1016\/0097-3165(73)90012-5_BIB15_1","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1112\/jlms\/s1-37.1.152","article-title":"Longest simple paths in polyhedral graphs","volume":"37","author":"Gr\u00fcnbaum","year":"1962","journal-title":"J. London Math. Soc."},{"key":"10.1016\/0097-3165(73)90012-5_BIB15_2","doi-asserted-by":"crossref","first-page":"744","DOI":"10.4153\/CJM-1963-071-3","article-title":"The number of hexagons and the simplicity of geodesics on certain polyhedra","volume":"15","author":"Gr\u00fcnbaum","year":"1963","journal-title":"Canad. J. Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB16_1","doi-asserted-by":"crossref","first-page":"69","DOI":"10.21136\/CPM.1968.108658","article-title":"A note on paths in quadrangular polyhedral graphs","volume":"93","author":"Jucovi\u010d","year":"1968","journal-title":"\u010casopis P\u011bst. Mat."},{"key":"10.1016\/0097-3165(73)90012-5_BIB16_2","series-title":"On the measure of inscribability of 3-polytopes","author":"Jucovi\u010d","year":"1972"},{"key":"10.1016\/0097-3165(73)90012-5_BIB17","series-title":"\u00dcber l\u00e4ngste Kreise in fl\u00e4chenregul\u00e4ren Polyedergraphen","author":"Jucovi\u010d","year":"1972"},{"key":"10.1016\/0097-3165(73)90012-5_BIB18","series-title":"Internat. Kolloq. Manebach, 1967","first-page":"91","article-title":"\u00dcber l\u00e4ngste Kreise in regul\u00e4ren Graphen, \u201cBeitr\u00e4ge zur Graphentheorie\u201d","author":"Lang","year":"1968"},{"key":"10.1016\/0097-3165(73)90012-5_BIB19","doi-asserted-by":"crossref","first-page":"522","DOI":"10.2307\/2314879","article-title":"Hamilton circuits of convex trivalent polyhedra (up to 18 vertices)","volume":"74","author":"Lederberg","year":"1967","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/0097-3165(73)90012-5_BIB20","series-title":"\u201cTheory of Graphs and Its Applications\u201d (Proc. Symp. Smolenice, 1963)","first-page":"143","article-title":"Simple paths on polyhedra","author":"Moon","year":"1964"},{"key":"10.1016\/0097-3165(73)90012-5_BIB21","doi-asserted-by":"crossref","first-page":"629","DOI":"10.2140\/pjm.1963.13.629","article-title":"Simple paths on polyhedra","volume":"13","author":"Moon","year":"1963","journal-title":"Pacific J. Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB22","series-title":"The Four-Color Problem","author":"Ore","year":"1967"},{"key":"10.1016\/0097-3165(73)90012-5_BIB23","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF02392080","article-title":"Facets and nonfacets of convex polytopes","volume":"119","author":"Perles","year":"1967","journal-title":"Acta Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB24","doi-asserted-by":"crossref","first-page":"367","DOI":"10.2307\/1968338","article-title":"Circuits upon polyhedra","volume":"33","author":"Reynolds","year":"1932","journal-title":"Ann. of Math."},{"key":"10.1016\/0097-3165(73)90012-5_BIB25","series-title":"Hamiltonian circuits in certain prisms","author":"Rosenfeld","year":"1972"},{"key":"10.1016\/0097-3165(73)90012-5_BIB26","doi-asserted-by":"crossref","first-page":"2","DOI":"10.2307\/2978124","article-title":"Thirteen colorful variations on Guthrie's four-color conjecture","volume":"79","author":"Saaty","year":"1972","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/0097-3165(73)90012-5_BIB27","first-page":"1","article-title":"Polyeder und Raumeinteilungen","volume":"3","author":"Steinitz","year":"1922","journal-title":"Encyklop\u00e4die der mathematischen Wissenschaften"},{"key":"10.1016\/0097-3165(73)90012-5_BIB28_1","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1112\/jlms\/s1-21.2.98","article-title":"On Hamiltonian circuits","volume":"21","author":"Tutte","year":"1946","journal-title":"J. London Math. Soc."},{"key":"10.1016\/0097-3165(73)90012-5_BIB28_2","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1090\/S0002-9947-1956-0081471-8","article-title":"A theorem on planar graphs","volume":"82","author":"Tutte","year":"1956","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/0097-3165(73)90012-5_BIB28_3","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/BF02020951","article-title":"A non-Hamiltonian planar graph","volume":"11","author":"Tutte","year":"1960","journal-title":"Acta Math. Acad. Sci. Hungar."},{"key":"10.1016\/0097-3165(73)90012-5_BIB29","series-title":"Kreise in Graphen","author":"Voss","year":"1972"},{"key":"10.1016\/0097-3165(73)90012-5_BIB30_1","first-page":"163","article-title":"Ein kubischer, planarer, zyklisch f\u00fcnffach zusammenh\u00e4ngender Graph, der keinen Hamiltonkreis besitzt","volume":"11","author":"Walther","year":"1965","journal-title":"Wiss. Z. Techn. Hochsch. Ilmenau"},{"key":"10.1016\/0097-3165(73)90012-5_BIB30_2","article-title":"\u00dcber das Problem der Existenz von Hamiltonkreisen in planaren, regul\u00e4ren Graphen vom Grad 3, 4, und 5","author":"Walther","year":"1966"},{"key":"10.1016\/0097-3165(73)90012-5_BIB30_3","first-page":"391","article-title":"\u00dcber die Anzahl der Knotenpunkte eines l\u00e4ngsten Kreises in planaren, kubischen, dreifach knotenzusammenh\u00e4ngenden Graphen","volume":"2","author":"Walther","year":"1967","journal-title":"Studia Sci. Math. Hungar."},{"key":"10.1016\/0097-3165(73)90012-5_BIB30_4","first-page":"139","article-title":"\u00dcber Extremalkreise in regul\u00e4ren Landkarten","volume":"15","author":"Walther","year":"1969","journal-title":"Wiss. Z. Techn. Hochsch. Ilmenau"},{"key":"10.1016\/0097-3165(73)90012-5_BIB30_5","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1002\/mana.19690390407","article-title":"\u00dcber das Problem der Existenz von Hamiltonkreisen in planaren, regul\u00e4ren Graphen","volume":"39","author":"Walther","year":"1969","journal-title":"Math. Nachr."},{"key":"10.1016\/0097-3165(73)90012-5_BIB31","doi-asserted-by":"crossref","first-page":"378","DOI":"10.2307\/1968197","article-title":"A theorem on graphs","volume":"32","author":"Whitney","year":"1931","journal-title":"Ann. of Math."}],"container-title":["Journal of Combinatorial Theory, Series A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0097316573900125?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0097316573900125?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,7,4]],"date-time":"2021-07-04T23:39:22Z","timestamp":1625441962000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0097316573900125"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1973,5]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1973,5]]}},"alternative-id":["0097316573900125"],"URL":"https:\/\/doi.org\/10.1016\/0097-3165(73)90012-5","relation":{},"ISSN":["0097-3165"],"issn-type":[{"value":"0097-3165","type":"print"}],"subject":[],"published":{"date-parts":[[1973,5]]}}}