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Graphs with large total domination number

✍ Scribed by Michael A. Henning


Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
246 KB
Volume
35
Category
Article
ISSN
0364-9024

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πŸ“œ SIMILAR VOLUMES


Domination critical graphs with higher i
✍ Ao, S.; Cockayne, E.J.; MacGillivray, G.; Mynhardt, C.M. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 348 KB πŸ‘ 2 views

We show that for each k L 4 there exists a connected k-domination critical graph with independent domination number exceeding k, thus disproving a conjecture of Sumner and Blitch ( J Cornbinatorial Theory B 34 (19831, 65-76) in all cases except k = 3.

Total domination in graphs with minimum
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A set S of vertices of a graph G is a total dominating set, if every vertex of V (G) is adjacent to some vertex in S. The total domination number of G, denoted by Ξ³ t (G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at leas

Total interval number for graphs with bo
✍ Kostochka, Alexander V.; West, Douglas B. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 90 KB πŸ‘ 1 views

The total interval number of an n-vertex graph with maximum degree βˆ† is at most (βˆ†+1/βˆ†)n/2, with equality if and only if every component of the graph is K βˆ†,βˆ† . If the graph is also required to be connected, then the maximum is βˆ†n/2 + 1 when βˆ† is even, but when βˆ† is odd it exceeds [βˆ† + 1/(2.5βˆ† + 7.7

Total colorings of planar graphs with la
✍ Borodin, O. V.; Kostochka, A. V.; Woodall, D. R. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 97 KB πŸ‘ 2 views

It is proved that a planar graph with maximum degree βˆ† β‰₯ 11 has total (vertex-edge) chromatic number βˆ† + 1.

Convexity of minimal total dominating fu
✍ Yu, Bo πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 122 KB πŸ‘ 1 views

A total dominating function (TDF) of a graph G = (V, E) is a function f : V β†’ [0, 1] such that for each v ∈ V , the sum of f values over the open neighbourhood of v is at least one. Zero-one valued TDFs are precisely the characteristic functions of total dominating sets of G. We study the convexity

Induced trees in graphs of large chromat
✍ Scott, A. D. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 134 KB πŸ‘ 1 views

GyΓ‘rfΓ‘s and Sumner independently conjectured that for every tree T and integer k there is an integer f (k, T ) such that every graph G with Ο‡(G) > f(k, t) contains either K k or an induced copy of T . We prove a `topologicalΒ΄version of the conjecture: for every tree T and integer k there is g(k, T )