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Regular totally domatically full graphs

✍ Scribed by Bohdan Zelinka


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
564 KB
Volume
86
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


Domatically critical and domatically ful
✍ Douglas F. Rall πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 396 KB

A subset, D, of the vertex set of a graph G is called a dominating set of G if each vertex of G is either in D or adjacent to some vertex in D. The maximum cardinality of a partition of the vertex set of G into dominating sets is the domatic number of G, denoted d(G). G is said to be domatically cri

The total {k}-domatic number of a graph
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Total colouring regular bipartite graphs
✍ Colin J.H. McDiarmid; AbdΓ³n SΓ‘nchez-Arroyo πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 437 KB

The total chromatic number of an arbitrary graph is the smallest number of colours needed to colour the edges and vertices of the graph so that no two adjacent or incident elements of the graph receive the same colour. In this paper we prove that the problem of determining the total chromatic number

On antichain intersection numbers, total
✍ Morimasa Tsuchiya πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 742 KB

In this paper, we consider total clique covers and intersection numbers on multifamilies. We determine the antichain intersection numbers of graphs in terms of total clique covers. From this result and some properties of intersection graphs on multifamilies, we determine the antichain intersection n

The total chromatic number of regular gr
✍ J.K. Dugdale; A.J.W. Hilton πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 705 KB

We show that a regular graph G of order at least 6 whose complement c is bipartite has total chromatic number d(G) + 1 if and only if (i) G is not a complete graph, and (ii) G#K when n is even. As an aid in"';he proof of this, we also show that , for n>4, if the edges of a Hamiltonian path of Kzn a

Total chromatic number of regular graphs
✍ K.H. Chew πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 695 KB

The total chromatic number XT(G) of a graph G is the least number of colours needed to colour the edges and vertices of G so that no incident or adjacent elements receive the same colour. This paper shows that if G is odd order and regular of degree d > [(&? -1)/6]1 V(G)/, then a necessary and suffi