Zhang–Liu–Wang conjecture on the adjacent vertex distinguishing chromatic index
Zhang–Liu–Wang conjecture on the adjacent vertex distinguishing chromatic index
Let be a finite simple graph with no isolated vertices. Write and for its vertex and edge sets, let be its maximum degree, and let denote the smallest number of colors in an adjacent vertex distinguishing edge coloring of . A graph is normal if it contains no isolated edges. Zhang–Liu–Wang's conjecture. If is a connected normal graph different from a -cycle and satisfies , then
The conjecture concerns an upper bound for the adjacent vertex distinguishing chromatic index in terms of maximum degree. The supplied source does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Lianzhu Zhang, Weifan Wang and Ko-Wei Lih, “An improved upper bound on the adjacent vertex distinguishing chromatic index of a graph”, arXiv:1208.2315 (2012).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.