216 research outputs found
Remarks on minus (signed) total domination in graphs
Author name used in this publication: T.C.E. ChengAuthor name also used in this publication: E.F. Shan2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
New bounds on the signed total domination number of graphs
In this paper, we study the signed total domination number in graphs and
present new sharp lower and upper bounds for this parameter. For example by
making use of the classic theorem of Turan, we present a sharp lower bound on
this parameter for graphs with no complete graph of order r+1 as a subgraph.
Also, we prove that n-2(s-s') is an upper bound on the signed total domination
number of any tree of order n with s support vertices and s' support vertives
of degree two. Moreover, we characterize all trees attainig this bound.Comment: This paper contains 11 pages and one figur
Minus total domination in graphs
summary:A three-valued function defined on the vertices of a graph is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every , , where consists of every vertex adjacent to . The weight of an MTDF is , over all vertices . The minus total domination number of a graph , denoted , equals the minimum weight of an MTDF of . In this paper, we discuss some properties of minus total domination on a graph and obtain a few lower bounds for
Global Domination Stable Graphs
A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal
Multipartite hypergraphs achieving equality in Ryser's conjecture
A famous conjecture of Ryser is that in an -partite hypergraph the
covering number is at most times the matching number. If true, this is
known to be sharp for for which there exists a projective plane of order
. We show that the conjecture, if true, is also sharp for the smallest
previously open value, namely . For , we find the minimal
number of edges in an intersecting -partite hypergraph that has
covering number at least . We find that is achieved only by linear
hypergraphs for , but that this is not the case for . We
also improve the general lower bound on , showing that .
We show that a stronger form of Ryser's conjecture that was used to prove the
case fails for all . We also prove a fractional version of the
following stronger form of Ryser's conjecture: in an -partite hypergraph
there exists a set of size at most , contained either in one side of
the hypergraph or in an edge, whose removal reduces the matching number by 1.Comment: Minor revisions after referee feedbac
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