7 papers
Frugal coloring in planar graphs with maximum degree 4 and 5
Boštjan Brešar, Přemysl Holub, Marko Jakovac +1
A proper coloring of vertices of a graph is called -frugal if no color appears more than times in the neighborhood of any vertex of . While -frugal coloring coinci…
On the Burning Game: Nordhaus-Gaddum Bounds and Graph Products
Nina Chiarelli, Vesna Iršič Chenoweth, Marko Jakovac +2
We continue research on the burning game on graphs. Given a graph , two players, Burner and Staller, take turns in selecting vertices of to burn. All burned vertices spread…
A variety of the mutual-visibility coloring problem for graphs
Saneesh Babu, Marko Jakovac, Dorota Kuziak +2
This paper explores variations of vertex-coloring problems defined on graph visibility properties. It introduces and studies the dual, outer, and total mutual-visibility chromatic…
Settling the total domination-annihilation conjecture for graphs with minimum degree two
Marko Jakovac
The total domination number of a graph is the minimum cardinality of a set such that every vertex of has a neighbor in . The annihilation numb…
Sequence b-colorings in graphs
Marko Jakovac, Michael S. Lang
We introduce and begin the study of sequence b-colorings, a natural generalization of the classical notion of b-colorings introduced by Irving and Manlove in 1999. In a sequence b-…
The burning game on graphs
Nina Chiarelli, Vesna Iršič, Marko Jakovac +2
Motivated by the burning and cooling processes, the burning game is introduced. Two players (Burner and Staller) play the game on a graph by alternately selecting vertices of $…
-packing colorings of distance graphs with distance sets of cardinality
Boštjan Brešar, Jasmina Ferme, Přemysl Holub +2
For a non-decreasing sequence of positive integers, a partition of the vertex set of a graph into subsets , such that vertices in …