## Abstract Weakening the notion of a strong (induced) matching of graphs, in this paper, we introduce the notion of a semistrong matching. A matching __M__ of a graph __G__ is called semistrong if each edge of __M__ has a vertex, which is of degree one in the induced subgraph __G__[__M__]. We stre
A generalization of edge-coloring in graphs
✍ Scribed by S. Louis Hakimi; Oded Kariv
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 754 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Bounds are given on the number of colors required to color the edges of a graph (multigraph) such that each color appears at each vertex u at most m(u) times. The known results and proofs generalize in natural ways. Certain new edge-coloring problems, which have no counterparts when m(u) = 1 for all u E V, are studied.
📜 SIMILAR VOLUMES
A computer code and nonnumerical algorithm are developed to construct the edge group of a graph and to enumerate the edge colorings of graphs of chemical interest. The edge colorings of graphs have many applications in nuclear magnetic resonance (NMR), multiple quantum NMR, enumeration of structural
Most of the general families of large considered graphs in the context of the so-called (⌬, D) problem-that is, how to obtain graphs with maximum order, given their maximum degree ⌬ and their diameter D-known up to now for any value of ⌬ and D, are obtained as product graphs, compound graphs, and ge
## Abstract 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
An __acyclic edge‐coloring__ of a graph is a proper edge‐coloring such that the subgraph induced by the edges of any two colors is acyclic. The __acyclic chromatic index__ of a graph __G__ is the smallest number of colors in an acyclic edge‐coloring of __G__. We prove that the acyclic chromatic inde