We show that the first problem is NP-complete and that the latter is polynomial.doi:10.1002/jgt.3190180509J. G. GimbelK. B. ReidJohn Wiley & Sons, Ltd.Journal of Graph Theory
Problem : You are given a connected graph with N nodes and M edges, graph does not contain multiple edges and self loops. An independent set of nodes is the set in which no two nodes are connected to each other. You need to find the largest independent set. Constraints : 3 <= N <=...
The extended line graph H of a graph H has V (H ) = E(H ) and two edges e and f of H are adjacent in H if (1) e = f , or (2) e and f share a common vertex, or (3) e and f are opposite edges of a 4-cycle in G. Theorem 5.3 ([7]). Let H be the extended...
A maximal outerplanar graph cannot have an independent 3-dominating set. Of course, the condition of maximality cannot be omitted here; the simplest examples showing this are the stars with at least three edges. The next lemma presents some useful properties of 2-trees having an independent 3-...
Let G=(V,E) be a finite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D o... CL Lu,MT Ko,CY Tang - 《Discrete Applied Mathematics》 被引量: 85发表: 2002年 Global Alliances and Independent Domination...
graph of a torus network is 6-regular, whether there exist 3-CISTs is an open question. In this article, we established the relationship between the completely independent spanning trees in the line graph and the edge division of the original graph. By dividing the edges of the torus ...
Let us assign independent, exponentially distributed random edge lengths to the edges of an undirected graph. Lyons, Pemantle, and Peres (1999, J. Combin. ... L. Lovász - 《J. Comb. Theory, Ser:a》 被引量: 0发表: 2001年 Polylog-time and near-linear work approximation scheme for undi...
Now let us show that G′ is an S2,2,2-free subcubic graph. The fact that G′ is subcubic is obvious. Assume to the contrary that it contains an induced subgraph H isomorphic to S2,2,2. If H contains none of the edges ab and cd, then clearly H is also an induced S2,2,2 in...
The 27th Workshop on Combinatorial Mathematics and Computation Theory Mutually Independent Hamiltonian Cycle of Burnt Pancake Graphs= be a graph of order n. A Hamiltonian cycle of G is a cycle contains every vertex in G. Two ... Y Lai,D Yu,GV Let 被引量: 0发表: 2013年 MUTUALLY INDEPEND...
Summary: Consider a packet walking along a directed graph with each node having two edges directed out. The packet is headed towards one of $N$ destinations, chosen according to a probability distribution $p$. At each step, the packet is forced to use a nonpreferred edge with some probabili...