On (s,t)-supereulerian graphs in locally highly connected graphs
نویسندگان
چکیده
منابع مشابه
On (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 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 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 کاملSupereulerian graphs and matchings
A graph G is called supereulerian if G has a spanning Eulerian subgraph. Let α(G) be the maximum number of independent edges in the graph G. In this paper, we show that if G is a 2-edge-connected simple graph and α(G) ≤ 2, then G is supereulerian if and only if G is not K2,t for some odd number t . © 2011 Elsevier Ltd. All rights reserved.
متن کاملOn extremal k-supereulerian graphs
A graph G is called k-supereulerian if it has a spanning even subgraph with at most k components. In this paper, we prove that any 2-edge-connected loopless graph of order n is ⌈(n − 2)/3⌉-supereulerian, with only one exception. This result solves a conjecture in [Z. Niu, L. Xiong, Even factor of a graphwith a bounded number of components, Australas. J. Combin. 48 (2010) 269–279]. As applicatio...
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: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.08.012