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- Paul A. Catlin, Jerrold W. Grossman, Arthur M. Hobbs, Hong-Jian Lai
- Discrete Applied Mathematics
- 1992

- Arthur M. Hobbs, Brian A. Bourgeois, Jothi Kasiraj
- Discrete Mathematics
- 1987

- Paul A. Catlin, Arthur M. Hobbs, Hong-Jian Lai
- Discrete Mathematics
- 2001

In previous papers, Catlin introduced four functions, denoted S O , S R , S C , and S H , between sets of ÿnite graphs. These functions proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero k-ows for a ÿxed integer k ¿ 3. Unfortunately, a subtle error caused several… (More)

- Arthur M. Hobbs, Edward F. Schmeichel
- Discrete Mathematics
- 1982

- Arthur M. Hobbs, Lavanya Kannan, Hong-Jian Lai, Hongyuan Lai, Guoqing Weng
- Discrete Applied Mathematics
- 2010

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: Keywords: Balanced graphs 1-balanced graphs Cartesian product of graphs Web graphs a b… (More)

- Arthur M. Hobbs
- 2010

In this paper we show that the connectivity of the kth power of a graph of connectivity m is at least km if the kth power of the graph is not a complete graph. Also, we. prove th at removing as many as k-2 vertices from the kth power of a graph (k ;;. 3) leaves a Hamiltonian graph, and that removing as many as k-3 vertices from the kth power of a graph… (More)

- Lavanya Kannan, Arthur M. Hobbs, Hong-Jian Lai, Hongyuan Lai
- Discrete Applied Mathematics
- 2009

- Paul Erdös, Arthur M. Hobbs
- J. Comb. Theory, Ser. B
- 1977

In this paper we prove that if k is an integer no less than 3, and if G is a two-connected graph with 2n-a vertices, a E {0, 1}, which is regular of degree n-k, then G is Hamiltonian if a = 0 and n > k 2 + k + 1 or if a = I and n > 2k 2-3k =, 3. We use the notation and terminology of [1]. Gordon [4] has proved that there are only a small number of… (More)