Arthur M. Hobbs

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Let the reals be extended to include oo with o~ > r for every real nuraber r. Given an extended real number r, a property P(r) of graphs is super-hereditary if, whenever graph G has property P(r) and H is a subgraph of G, then H has property P(s) with s I> r. Notice that girth is a super-hereditary property if a forest has girth oo. In this paper, we prove(More)
In this paper, we show that if n 14 and if G is a Z-connected graph with 2n or 2n1 vertices which is regular of degree n -2, then G is Hamiltonian if and only if G is not the Petersen graph. We use the terminology of Behzad and Chartrand [2]. In particular, a set of vertices in a graph is independent if no two of the vertices in the set are adjacent. A(More)
In previous papers, Catlin introduced four functions, denoted S, S, S , and S , between sets of nite graphs. These functions proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero kows for a xed integer k¿ 3. Unfortunately, a subtle error caused several theorems(More)
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)
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)
Let G be a non-trivial, loopless graph and for each non-trivial subgraph H of G, let g(H) = |E(H)| |V(H)|−ω(H) . The graph G is 1-balanced if γ(G), the maximum among g(H), taken over all nontrivial subgraphs H of G, is attained when H = G. This quantity γ(G) is called the fractional arboricity of the graph G. The value γ(G) appears in a paper by Picard and(More)