Author

Sara Al Hajjar

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Aug 2026

An Improvement of the 2-Distance Chromatic Number of Planar Graphs with Maximum Degree at Most 6

A 2-distance [Formula: see text]-coloring of a graph is a proper coloring of the vertices of the graph using [Formula: see text] colors such that any two vertices at distance two or less get distinct colors. The 2-distance chromatic number of a graph [Formula: see text], denoted as [Formula: see text], is the minimum i...

Sara Al Hajjar · Discrete Mathematics, Algori... · 0 citations

Preprint Jul 2026

List Coloring of the Square of 4-Irregular Graphs

The square of a graph $G$ is the graph obtained from $G$ after adding an edge between any two vertices of distance $2$. A $k$-irregular graph is a graph with maximum degree $k$ such that vertices of degree $k$ are not adjacent. A \textit{list assignment} of a graph is a function $L$ that assigns to each vertex a list o...

Sara Al Hajjar · 0 citations

Preprint Aug 2026

2-Distance Coloring of 4-Irregular Planar Graphs

A $k$-irregular graph is a graph with maximum degree $k$ such that vertices of degree $k$ are not adjacent. A $2$-distance $k$-coloring of a graph is a coloring of the vertices using $k$ colors in which any two vertices at distance at most $2$ receive distinct colors. The $2$-distance chromatic number of $G$, denoted b...

Sara Al Hajjar · 0 citations