@article{discovery10192107,
       publisher = {Society for Industrial and Applied Mathematics},
          volume = {38},
           month = {June},
            note = {This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.},
           pages = {1239--1249},
         journal = {SIAM Journal on Discrete Mathematics},
          number = {2},
           title = {The Rainbow Saturation Number Is Linear},
            year = {2024},
            issn = {0895-4801},
        keywords = {edge-coloring, Mathematics, Mathematics, Applied, Physical Sciences, rainbow, saturation, Science \& Technology},
          author = {Behague, Natalie and Johnston, Tom and Letzter, Shoham and Morrison, Natasha and Ogden, Shannon},
        abstract = {Given a graphH, we say that an edge-colored graphGisH-rainbow saturated ifit  does  not  contain  a  rainbow  copy  ofH,  but  the  addition  of  any  nonedge  in  any  color  creates  arainbow  copy  ofH.   The  rainbow  saturation  number  rsat(n,H)  is  the  minimum  number  of  edgesamong allH-rainbow saturated edge-colored graphs onnvertices.  We prove that for any nonemptygraphH, the rainbow saturation number is linear inn, thus proving a conjecture of Gir{$\backslash$}{\texttt{\char126}}ao, Lewis,and Popielarz.  In addition, we give an improved upper bound on the rainbow saturation number ofthe complete graph, disproving a second conjecture of Gir{$\backslash$}{\texttt{\char126}}ao, Lewis, and Popielarz.},
             url = {http://dx.doi.org/10.1137/23m1566881}
}