5 papers
The odd independence number of graphs, II: Finite and infinite grids and chessboard graphs
Yair Caro, Mirko Petruševski, Riste Škrekovski +1
An odd independent set in a graph is an independent set of vertices such that, for every vertex , either or $|N(v) \cap…
The odd independence number of graphs, I: Foundations and classical classes
Yair Caro, Mirko Petruševski, Riste Škrekovski +1
An odd independent set in a graph is an independent set of vertices such that, for every vertex , either or $|N(v) \cap…
On Graph Odd Edge-Colorings and Odd Edge-Coverings
Xiao-Chuan Liu, Mirko Petruševski, Xu Yang
An odd -edge-coloring of a graph is a (not necessarily proper) edge-coloring with at most colors such that each non-empty color class induces a graph in which every vert…
On chromatic vertex stability of 3-chromatic graphs with maximum degree 4
Martin Knor, Mirko Petruševski, Riste Škrekovski
The (independent) chromatic vertex stability ($\ivs(G)$) $\vs(G)$ is the minimum size of (independent) set such that . In this paper we construct i…
Colorings with neighborhood parity condition
Mirko Petruševski, Riste Škrekovski
In this short paper, we introduce a new vertex coloring whose motivation comes from our series on odd edge-colorings of graphs. A proper vertex coloring of graph is said to…