33 research outputs found
On edge-group choosability of graphs
In this paper, we study the concept of edge-group choosability of graphs. We
say that G is edge k-group choosable if its line graph is k-group choosable. An
edge-group choosability version of Vizing conjecture is given. The evidence of
our claim are graphs with maximum degree less than 4, planar graphs with
maximum degree at least 11, planar graphs without small cycles, outerplanar
graphs and near-outerplanar graphs
The Ramsey number of loose paths in 3-uniform hypergraphs
Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and
also loose paths were determined. Here we determine the 2-color Ramsey number
of 3-uniform loose paths when one of the paths is significantly larger than the
other: for every , we show that
R(\mathcal{P}^3_n,\mathcal{P}^3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.$