$N_2$-locally connected graphs and their upper embeddability
نویسندگان
چکیده
منابع مشابه
Connected Graphs and Their Connectivities
Let m and n be positive integers with n − 1 ≤ m ≤ ( n 2 ) and CG(m,n) be the set of all non-isomorphic connected graphs of order n and size m. The vertex-connectivity and the edge-connectivity of a graph G are denoted by κ(G) and λ(G), respectively. We prove that if π ∈ {κ, λ}, then there exist positive integers a and b such that {π(G) : G ∈ CG(m,n)} = {x ∈ Z : a ≤ x ≤ b}. Thus {π(G) : G ∈ CG(m...
متن کاملHamiltonian N2-locally connected claw-free graphs
A graph G is N2-locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryjác̆ek conjectured that every 3-connected N2-locally connected claw-free graph is hamiltonian. This conjecture is proved in this note.
متن کاملLocally connected spanning trees on graphs
A locally connected spanning tree of a graph G is a spanning tree T of G such that the set of all neighbors of v in T induces a connected subgraph of G for every v ∈ V (G). The purpose of this paper is to give linear-time algorithms for finding locally connected spanning trees on strongly chordal graphs and proper circular-arc graphs, respectively.
متن کاملLower Bounds for Locally Highly Connected Graphs
We propose a conjecture regarding the lower bound for the number of edges in locally k-connected graphs and we prove it for k = 2. In particular, we show that every connected locally 2-connected graph is M3-rigid. For the special case of surface triangulations, this fact was known before using topological methods. We generalize this result to all locally 2-connected graphs and give a purely com...
متن کاملOn (s, t)-supereulerian graphs in locally highly connected graphs
Given two nonnegative integers s and t , a graph G is (s, t)-supereulerian if for any disjoint sets X, Y ⊂ E(G) with |X | ≤ s and |Y | ≤ t , there is a spanning eulerian subgraph H of G that contains X and avoids Y . We prove that if G is connected and locally k-edge-connected, thenG is (s, t)-supereulerian, for any pair of nonnegative integers s and t with s+t ≤ k−1. We further show that if s ...
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: Czechoslovak Mathematical Journal
سال: 1991
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1991.102504