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A graph is supereulerian if it has a spanning Eulerian subgraph. Motivated by the Chinese Postman Problem, Boesch, Suffel, and Tindell ([2]) in 1997 proposed the supereulerian problem, which seeks a characterization of graphs that have spanning Eulerian subgraphs, and they indicated that this problem would be very difficult. Pulleyblank ([71]) later in 1979(More)
In this article, we first show that every 3-edge-connected graph with circumference at most 8 is supereulerian, which is then applied to show that a 3-connected claw-free graph without Z8 as an induced subgraph is Hamiltonian, where Z8 denotes the graph derived from identifying one end vertex of P9 (a path with 9 vertices) with one vertex of a triangle. The(More)
A classical result of Chvátal and Erdős says that the graph G with connectivity κ(G) not less than its independent number α(G) (i.e. κ(G) ≥ α(G)) is hamiltonian. In this paper, we show that the graph G with κ(G) ≥ α(G) − 1 is either supereulerian, or the Petersen graph, or the graphs obtained from K2,3 by adding at most one vertex in one edge of K2,3 and by(More)
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.
Let G be an undirected graph that is neither a path nor a cycle. Clark and Wormald [L.H. Clark, N.C. Wormald, Hamiltonian-like indices of graphs, ARS Combinatoria 15 (1983) 131–148] defined hc(G) to be the least integerm such that the iterated line graph Lm(G) is Hamilton-connected. Let diam(G) be the diameter of G and k be the length of a longest path(More)
In this paper, we focus on the asymptotic capacity and delay, and their tradeoffs in mobile ad hoc networks (MANETs). As we all know, some fixed rate communication models such as the protocol model and the physical model have been studied in the past. However, our work aims to investigate the impact of an adaptive rate communication model on capacity-delay(More)
In this paper, we study capacity scaling laws of the deterministic dissemination (DD) in random wireless networks under the generalized physical model (GphyM). This is truly not a new topic. Our motivation to readdress this issue is two-fold: Firstly, we aim to propose a more general result to unify the network capacity for general homogeneous random models(More)
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.(More)
In this paper, we study capacity scaling laws of the deterministic dissemination (DD) in random wireless networks under the generalized physical model (GphyM). This is truly not a new topic. Our motivation to readdress this issue is two-fold: Firstly, we aim to propose a more general result to unify the network capacity for general homogeneous random models(More)
Abstract—In this paper, we address the issue on measuring the transport difficulty for content dissemination in online social networks (OSNs). We define a new metric, called transport load, to measure the load imposed by the OSN on the carrier communication network. It involves two key factors: data arrival process at users and transport distance of(More)