A proper edge k-coloring is a mappingΦ:E(G)-→{1,2,...,k}such that any two adjacent edges receive different colors.A proper edge k-coloringΦof G is called acyclic if there are no bichromatic cycles in G.The acyclic ...
supported by the RFBR and the NFSC(Project No.20-51-53013);supported by the NNSF of China(No.12171126).
Earlier it was proved that some distance-regular graphs of diameter 3 with c_(2)=2 do not exist.Distance-regular graphΓwith intersection array{17,16,10;1,2,8}has strongly regular graphΓ_(3)(pseudo-geometric graph fo...
An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles.The acyclic edge chromatic number of a graph G is the minimum number k such that there exists an acyclic edge c...
Suppose that G is a planar graph with maximum degree △. In this paper it is proved that G is total-(△ + 2)-choosable if (1) △ ≥ 7 and G has no adjacent triangles (i.e., no two triangles are incident with a c...