{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T16:49:19Z","timestamp":1648745359903},"reference-count":6,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T00:00:00Z","timestamp":1584403200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T00:00:00Z","timestamp":1584403200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2020,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A cycle is 2-<jats:italic>colored<\/jats:italic> if its edges are properly colored by two distinct colors. A (<jats:italic>d<\/jats:italic>,\u00a0<jats:italic>s<\/jats:italic>)-<jats:italic>edge colorable graph<\/jats:italic><jats:italic>G<\/jats:italic> is a <jats:italic>d<\/jats:italic>-regular graph that admits a proper <jats:italic>d<\/jats:italic>-edge coloring in which every edge of <jats:italic>G<\/jats:italic> is in at least <jats:inline-formula><jats:alternatives><jats:tex-math>$$s-1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>s<\/mml:mi><mml:mo>-<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> 2-colored 4-cycles. Given a (<jats:italic>d<\/jats:italic>,\u00a0<jats:italic>s<\/jats:italic>)-edge colorable graph <jats:italic>G<\/jats:italic> and a list assigment <jats:italic>L<\/jats:italic> of forbidden colors for the edges of <jats:italic>G<\/jats:italic> satisfying certain sparsity conditions, we prove that there is a proper <jats:italic>d<\/jats:italic>-edge coloring of <jats:italic>G<\/jats:italic> that avoids <jats:italic>L<\/jats:italic>, that is, a proper edge coloring <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varphi$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c6<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula> of <jats:italic>G<\/jats:italic> such that <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varphi (e) \\notin L(e)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>\u03c6<\/mml:mi><mml:mo>(<\/mml:mo><mml:mi>e<\/mml:mi><mml:mo>)<\/mml:mo><mml:mo>\u2209<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>(<\/mml:mo><mml:mi>e<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula> for every edge <jats:italic>e<\/jats:italic> of <jats:italic>G<\/jats:italic>. Additionally, this paper also contains a discussion of graphs belonging to the family of (<jats:italic>d<\/jats:italic>,\u00a0<jats:italic>s<\/jats:italic>)-edge colorable graphs.<\/jats:p>","DOI":"10.1007\/s00373-020-02158-9","type":"journal-article","created":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T09:03:40Z","timestamp":1584435820000},"page":"853-864","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Restricted Colorings of $$\\text{(d,s)}$$-Edge Colorable Graphs"],"prefix":"10.1007","volume":"36","author":[{"given":"Lan Anh","family":"Pham","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,3,17]]},"reference":[{"issue":"1","key":"2158_CR1","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1006\/jctb.1995.1011","volume":"63","author":"Fred Galvin","year":"1995","unstructured":"Galvin, Fred: The list chromatic index of a bipartite multigraph. 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