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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 Z 8 as an induced subgraph is Hamiltonian, where Z 8 denotes the graph derived from identifying one end vertex of P 9 (a path with 9 vertices) with one vertex of a triangle.(More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t A graph G is called supereulerian if G has a spanning Eulerian(More)
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)
A classical result of Chvátal and Erd˝ os 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 K 2,3 by adding at most one vertex in one edge of K 2,3(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)
Keywords: Hamilton-connected index Iterated line graph Diameter Maximum degree Connectivity a b s t r a c t Let G be an undirected graph that is neither a path nor a cycle.like indices of graphs, ARS Combinatoria 15 (1983) 131–148] defined hc(G) to be the least integer m such that the iterated line graph L m (G) is Hamilton-connected. Let diam(G) be the(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 twofold: 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 graph with a bounded number of components, Australas. J. As(More)
—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 messages.(More)