Construction of class 2 graphs with maximum vertex degree 3

Faster computation of maximum independent set and parameterized vertex cover for graphs with maximum degree 3

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

Laplacian Integral Graphs with Maximum Degree 3

A graph is said to be Laplacian integral if the spectrum of its Laplacian matrix consists entirely of integers. Using combinatorial and matrix-theoretic techniques, we identify, up to isomorphism, the 21 connected Laplacian integral graphs of maximum degree 3 on at least 6 vertices.

Acyclic Vertex Coloring of Graphs of Maximum Degree 4

The acyclic chromatic number of a graph G, denoted a(G), is the minimum number of colors required to properly color the vertices of a graph such that there are no bichromatic cycles. The concept of acyclic coloring of a graph was introduced by [5] and is further studied in the last two decades in several works. Kostochka [6] proves that determining it is an NP-complete problem. Given the comput...

Acyclic Vertex Coloring of Graphs of Maximum Degree

An acyclic vertex coloring of a graph is a proper vertex coloring such that there are no bichromatic cycles. The acyclic chromatic number of G, denoted a(G), is the minimum number of colors required for acyclic vertex coloring of graph G = (V,E). For a family F of graphs, the acyclic chromatic number of F , denoted by a(F), is defined as the maximum a(G) over all the graphs G ∈ F . In this pape...