Edge-coloring series-parallel multigraphs
نویسندگان
چکیده
We give a simpler proof of Seymour’s Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colored with a given number of colors.
منابع مشابه
A Linear Algorithm for Edge-Coloring Series-Parallel Multigraphs
Many combinatorial problems can be efficiently solved for series]parallel multigraphs. However, the edge-coloring problem of finding the minimum number of colors required for edge-coloring given graphs is one of a few well-known combinatorial problems for which no efficient algorithms have been obtained for series]parallel multigraphs. This paper gives a linear algorithm for the problem on seri...
متن کاملAn NC Parallel Algorithm for Edge-Coloring Series-Parallel Multigraphs
Many combinatorial problems can be efficiently solved in parallel for series]parallel multigraphs. The edge-coloring problem is one of a few combinatorial problems for which no NC parallel algorithm has been obtained for series]parallel multigraphs. This paper gives an NC parallel algorithm for the Ž . Ž . problem on series]parallel multigraphs G. It takes O log n time with O Dnrlog n processor...
متن کاملAn Efficient Algorithm for Edge-Coloring Series-Parallel Multigraphs
Many combinatorial problems can be efficiently solved for series-parallel graphs or partial k-trees. The edge-coloring problem is one of a few combinatorial problems for which no efficient algorithms have been obtained for series-parallel multigraphs. This paper gives an algorithm which optimally edge-colors a given series-parallel multigraph in time O([V[z~), where V is the set of vertices and...
متن کاملOn Interval Non-Edge-Colorable Eulerian Multigraphs
An edge-coloring of a multigraph G with colors 1, . . . , t is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this note, we show that all Eulerian multigraphs with an odd number of edges have no interval coloring. We also give some methods for constructing of interval non-edge-colorable ...
متن کاملChromatic Edge Strength of Some Multigraphs
The edge strength s(G) of a multigraph G is the minimum number of colors in a minimum sum edge coloring of G. We give closed formulas for the edge strength of bipartite multigraphs and multicycles. These are shown to be classes of multigraphs for which the edge strength is always equal to the chromatic index.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1107.5370 شماره
صفحات -
تاریخ انتشار 2007