4 papers · 1 filter
On saturation problems for matchings with regularity constraints
Gang Yang, Zixuan Yang, Shenggui Zhang
A graph is -saturated if is -free but for any edge in the complement of the graph contains . Gerbner et al. (Discrete Math., 345 (2022), 112921) in…
On graphs without cycles of length 1 modulo 3
Yandong Bai, Binlong Li, Yufeng Pan +1
Burr and Erdős conjectured in 1976 that for every two integers satisfying that contains an even integer, an -vertex graph containing no cy…
Closures and heavy pairs for hamiltonicity
Wangyi Shang, Hajo Broersma, Shenggui Zhang +1
We say that a graph on vertices is --heavy if every induced subgraph of isomorphic to or contains two nonadjacent vertices with degree sum at least…
The absence of monochromatic triangle implies various properly colored spanning trees
Ruonan Li, Ruhui Lu, Xueli Su +1
An edge-colored graph is called properly colored if every two adjacent edges are assigned different colors. A monochromatic triangle is a cycle of length 3 with all the edges h…