A total perfect code in a graph is a subset of the graph's vertices with the property that each vertex in the graph is adjacent to exactly one vertex in the subset. We prove t...
Ghidewon Abay-Asmerom, Richard Hammack, Dewey T. T...
It is proved that, if G is a K4-minor-free graph with maximum degree 3, then G is totally 4-choosable; that is, if every element (vertex or edge) of G is assigned a list of 4 colo...
It is proved that, if G is a K4-minor-free graph with maximum degree 4, then G is totally ( + 1)-choosable; that is, if every element (vertex or edge) of G is assigned a list of ...
A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. The matching number of G is the maximum cardinality of a matching of G. A set S o...
An interval total t coloring of a graph G is a total coloring of with colors 1, such that at least one vertex or edge of is colored by color − G 2, ,t… G , 1, 2, ,i i t= … ,...
Petros A. Petrosyan, Ani Shashikyan, Arman Yu. Tor...