Independent domination in triangle-free graphs
نویسندگان
چکیده
منابع مشابه
The independent domination number of maximal triangle-free graphs
A triangle-free graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. In this paper, we show that i(G) ≤ δ(G) ≤ n 2 for maximal triangle-free graph...
متن کاملIndependent domination in directed graphs
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
متن کاملIndependent dominating sets in triangle-free graphs
The independent domination number of a graph is the smallest cardinality of an independent set that dominates the graph. In this paper we consider the independent domination number of triangle-free graphs. We improve several of the known bounds as a function of the order and minimum degree, thereby answering conjectures of Haviland.
متن کاملCounting independent sets in triangle-free graphs
Ajtai, Komlós, and Szemerédi proved that for sufficiently large t every trianglefree graph with n vertices and average degree t has an independent set of size at least n 100t log t. We extend this by proving that the number of independent sets in such a graph is at least 2 1 2400 n t log . This result is sharp for infinitely many t, n apart from the constant. An easy consequence of our result i...
متن کاملIndependent sets in triangle-free cubic planar graphs
We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 38n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.07.010