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There are only a few values of <jats:italic>m<\/jats:italic>(<jats:italic>t<\/jats:italic>,\u00a0<jats:italic>r<\/jats:italic>) known, for instance <jats:inline-formula><jats:alternatives><jats:tex-math>$$m(3,3)=m(4,r)=1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>m<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mi>m<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$m(t,r) \\le r-2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>m<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>t<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for all <jats:inline-formula><jats:alternatives><jats:tex-math>$$t \\not = 5$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>t<\/mml:mi>\n                    <mml:mo>\u2260<\/mml:mo>\n                    <mml:mn>5<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$m(t,r) \\le r-3$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>m<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>t<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> if <jats:italic>r<\/jats:italic> is even. We prove that <jats:inline-formula><jats:alternatives><jats:tex-math>$$m(2l,r) \\le 3l - 6$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>m<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mi>l<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                    <mml:mi>l<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>6<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for every <jats:inline-formula><jats:alternatives><jats:tex-math>$$l \\ge 3$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>l<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$r \\ge 2 l$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mi>l<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00493-023-00078-9","type":"journal-article","created":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T17:02:22Z","timestamp":1703005342000},"page":"429-440","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs"],"prefix":"10.1007","volume":"44","author":[{"given":"Yulai","family":"Ma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davide","family":"Mattiolo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eckhard","family":"Steffen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Isaak H.","family":"Wolf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,12,19]]},"reference":[{"key":"78_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1002\/(SICI)1097-0118(199901)30:1<27::AID-JGT4>3.0.CO;2-Z","volume":"30","author":"S Gr\u00fcnewald","year":"1999","unstructured":"Gr\u00fcnewald, S., Steffen, E.: Chromatic-index-critical graphs of even order. 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