{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:28Z","timestamp":1740107128785,"version":"3.37.3"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T00:00:00Z","timestamp":1730937600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T00:00:00Z","timestamp":1730937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"TU Wien"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A <jats:italic>M<\/jats:italic> in a cubic graph <jats:italic>G<\/jats:italic> is a spanning subgraph of <jats:italic>G<\/jats:italic> such that every component of <jats:italic>M<\/jats:italic> is isomorphic to <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>K<\/mml:mi>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> or to <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_{1,3}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>K<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mn>1<\/mml:mn>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mn>3<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In view of snarks <jats:italic>G<\/jats:italic> with dominating cycle <jats:italic>C<\/jats:italic>, this is a natural generalization of perfect matchings since <jats:inline-formula><jats:alternatives><jats:tex-math>$$G \\setminus E(C)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>G<\/mml:mi>\n                    <mml:mo>\\<\/mml:mo>\n                    <mml:mi>E<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is a perfect pseudo-matching. Of special interest are such <jats:italic>M<\/jats:italic> where <jats:italic>G<\/jats:italic>\/<jats:italic>M<\/jats:italic> is planar because such <jats:italic>G<\/jats:italic> have a cycle double cover. We show that various well known classes of snarks contain planarizing perfect pseudo-matchings, and that there are at least as many snarks with planarizing perfect pseudo-matchings as there are cyclically <jats:inline-formula><jats:alternatives><jats:tex-math>$$5-$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>5<\/mml:mn>\n                    <mml:mo>-<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>edge-connected snarks.<\/jats:p>","DOI":"10.1007\/s00373-024-02844-y","type":"journal-article","created":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T16:07:27Z","timestamp":1730995647000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Perfect Pseudo-Matchings in Cubic Graphs"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8588-5212","authenticated-orcid":false,"given":"Herbert","family":"Fleischner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Behrooz Bagheri","family":"Gh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benedikt","family":"Klocker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"2844_CR1","doi-asserted-by":"crossref","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory. 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