Rainbow connection number and connected dominating sets
نویسندگان
چکیده
منابع مشابه
Rainbow Connection Number and Connected Dominating Sets
Rainbow connection number rc(G) of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we show that for every connected graph G, with minimum degree at least 2, the rainbow connection number is upper bounded by γc(G) + 2, where γc(G) is th...
متن کاملProper connection number and connected dominating sets
The proper connection number pc(G) of a connected graph G is defined as the minimum number of colors needed to color its edges, so that every pair of distinct vertices of G is connected by at least one path in G such that no two adjacent edges of the path are colored the same, and such a path is called a proper path. In this paper, we show that for every connected graph with diameter 2 and mini...
متن کاملConnected Dominating Sets
PROBLEM DEFINITION Consider a graph G = (V,E). A subset C of V is called a dominating set if every vertex is either in C or adjacent to a vertex in C. If, furthermore, the subgraph induced by C is connected, then C is called a connected dominating set. A connected dominating set with a minimum cardinality is called a minimum connected dominating set (MCDS). Computing a MCDS is an NP-hard proble...
متن کاملConnected Dominating Sets
Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks like mobile ad hoc networ...
متن کاملThe rainbow connection number of 2-connected graphs
The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most dn/2e. The bound is optimal.
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: Journal of Graph Theory
سال: 2011
ISSN: 0364-9024
DOI: 10.1002/jgt.20643