Finding Independent Sets inK4-Free 4-Regular Connected Graphs
نویسندگان
چکیده
Let G be a K4-free 4-regular connected graph with & vertices. Then G contains an independent set of vertices of cardinality at least (7&&4) 26. Furthermore, the proof will yield a polynomial-time algorithm which will return an independent set of cardinality at least (7&&4) 26 for any such graph. A family of K4 -free 4-regular connected graphs with maximum independent set of cardinality 3 11& is provided, so that the asymptotically sharp lower bound lies between 7 26 and 3 11 . We also provide a slight improvement over the best previously known result for triangle-free 5-regular graphs. 1997 Academic Press
منابع مشابه
Randomised Algorithms for Finding Small Weakly-Connected Dominating Sets of Regular Graphs
A weakly-connected dominating set, W, of a graph, G, is a dominating set such that the subgraph consisting of V (G) and all edges incident with vertices in W is connected. Finding a small weaklyconnected dominating set of a graph has important applications in clustering mobile ad-hoc networks. In this paper we introduce several new randomised greedy algorithms for finding small weakly-connected...
متن کاملOn connected k-domination in graphs
Let G = (V (G), E(G)) be a simple connected graph, and let k be a positive integer. A subset D ⊆ V (G) is a connected k-dominating set of G if its induced subgraph is connected and every vertex of V (G) −D is adjacent to at least k vertices of D. The connected k-domination number γ k(G) is the minimum cardinality among the connected k-dominating sets of G. In this paper, we give some properties...
متن کاملMatching Integral Graphs of Small Order
In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...
متن کاملConnected domination of regular graphs
A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either v ∈ D or there exists a vertex u ∈ D that is adjacent to v in G. Dominating sets of small cardinality are of interest. A connected dominating set C of a graph G is a dominating set of G such that the subgraph induced by the vertices of C in G is connected. A weakly-connected dominating set W of a g...
متن کاملExtremal H-colorings of trees and 2-connected graphs
For graphs G and H, an H-coloring of G is an adjacency preserving map from the vertices of G to the vertices of H. H-colorings generalize such notions as independent sets and proper colorings in graphs. There has been much recent research on the extremal question of finding the graph(s) among a fixed family that maximize or minimize the number of H-colorings. In this paper, we prove several res...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 71 شماره
صفحات -
تاریخ انتشار 1997