## 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
Transitive Edge Coloring of Graphs and Dimension of Lattices
✍ Scribed by András Gyárfás*
- Publisher
- Springer-Verlag
- Year
- 2002
- Tongue
- English
- Weight
- 248 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0209-9683
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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
For a graph G(V, E), if a proper k-edge coloring f is satisfied with C(u) # C(V) for UZ) E E(G), where C(u) = {f(~v) 1 UZI E E}, then f is called k-adjacent strong edge coloring of G. is abbreviated k-ASEC, and xbs(G) = min{k 1 k-ASEC of G} is called the adjacent strong edge chromatic number of G. I
## 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
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