๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The achromatic indices of the regular complete multipartite graphs

โœ Scribed by Nam-Po Chiang; Hung-Lin Fu


Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
272 KB
Volume
141
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis


In this paper, we study the achromatic indices of the regular complete multipartite graphs and obtain the following results:

(1) A good upper bound for the achromatic index of the regular complete multipartite graph which gives the exact values of an infinite family of graphs and solves a problem posed by Bouchet.

(2) An improved Bouchet coloring which gives the achromatic indices of another infinite family of regular complete multipartite graphs.


๐Ÿ“œ SIMILAR VOLUMES


The star-arboricity of the complete regu
โœ Yasukazu Aoki ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 331 KB

A subgraph H of a graph G is called a star-subgraph if each component of H is a star. The star-arboricify of G, denoted by sa(G), is the minimum number of star-subgraphs that partition the edges of G. In this paper we show that sa(G) is [r/21 + 1 or [r/2] + 2 for the complete r-regular multipartite

The chromatic index of complete multipar
โœ D. G. Hoffman; C. A. Rodger ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 266 KB

## Abstract We show that a complete multipartite graph is class one if and only if it is not eoverfull, thus determining its chromatic index.

On the euclidean dimension of a complete
โœ Hiroshi Maehara ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 272 KB

The euclidean dimension of a graph G, e(G), is the minimum n such that the vertices of G can be placed in euclidean n-space, R", in such a way that adjacent vertices have distance 1 and nonadjacent vertices have distances other than 1. Let G = K(n,, . , ns+,+J be a complete (s + t + u)-partite graph

The diameter of an orientation of a comp
โœ K.M. Koh; B.P. Tan ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 390 KB

For a graph G, let e(G) denote the minimum value of the diameters diamD of D, where D runs through all the orientations of G. In this paper, we obtain some results on e(G) for complete multipartite graphs G, which extend some known results due to Boesch and Tindell [1] and Maurer [4].

l-Regular rotations of the countably inf
โœ Mark Jungerman ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 998 KB

## All WWV . I-regular rotation of the infinite complete graph with countable vertex set is one in induced circuit is finite of kngth 1. I-regular rotations are exhibited for all 1 a 3. which Triangular rotations of finite graphs have been extensively studied. In particular, finding such rotation

On the Number of Nonisomorphic Orientabl
โœ Vladimir P. Korzhik; Heinz-Jurgen Voss ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 260 KB

In this paper we consider those 2-cell orientable embeddings of a complete graph K n+1 which are generated by rotation schemes on an abelian group 8 of order n+1, where a rotation scheme an 8 is defined as a cyclic permutation ( ; 1 , ; 2 , ..., ; n ) of all nonzero elements of 8. It is shown that t