Acyclic Edge-coloring of Sierpinski-like Graphs
نویسندگان
چکیده
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by χ′a(G). Sierpinski graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpinski gasket graphs Sn are the graphs naturally defined by the finite number of iterations that lead to the Sierpinski gasket. Sierpinski graph and Sierpinski gasket constitute Sierpinski-like graphs. We give algorithms for coloring the Sierpinski-like graphs acyclically using optimal set of colors. AMS Subject Classification: 05C15
منابع مشابه
A new approach to compute acyclic chromatic index of certain chemical structures
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $chi_a '(G)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. The maximum degree in $G$ denoted by $Delta(G)$, is the lower bound for $chi_a '(G)$. $P$-cuts introduced in this paper acts as a powerfu...
متن کاملOn Acyclic Vertex Coloring of Grid like graphs
d-dimensional partial tori are graphs that can be expressed as cartesian product of d graphs each of which is an induced path or cycle. Some well known graphs like d-dimensional hypercubes, meshes and tori are examples belong to this class. Muthu et al.[MNS06] have studied the problem of acyclic edge coloring for such graphs. We try to explore the acyclic vertex coloring problem for these graph...
متن کاملAcyclic edge coloring of 2-degenerate graphs
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a′(G). A graph is called 2-degenerate if any of its induced subgraph has a vertex of degree at most 2. The class of 2-degenerate graphs properly contain...
متن کاملAcyclic edge coloring of subcubic graphs
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using 5 colors. This result is tight since there are...
متن کاملAcyclic chromatic index of triangle-free 1-planar graphs
An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). A graph is 1-planar if it can be drawn on the plane such that every edg...
متن کامل