Connected Factors in Graphs ? a Survey

Connected Factors in Graphs - a Survey

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A Degree Condition For Graphs to Have Connected (g, f)-Factors

A Survey of Graphs Hamiltonian - Connected from a Vertex

A graph G is called hamiltonian-<:onnectedfrom a vertex v ifa hamiltonian path exists from v to every other vertex w ~ v. We present a survey of the main results known about such graphs, including a section on graphs uniquely hamiltonian-connected from a venex and a section on the computational complexity ofdetermining whether a given graph is hamiltonian-<:onnectedfrom a venex or uniquely hami...

connected graphs cospectral with a friendship graph

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

2-Factors in r-Connected {K1,k, P4}-Free Graphs

In [3], Faudree et.al. considered the proposition “Every {X, Y }-free graph of sufficiently large order has a 2-factor,” and they determined those pairs {X, Y } which make this proposition true. Their result says that one of them is {X, Y } = {K1,4, P4}. In this paper, we investigate the existence of 2-factors in r-connected {K1,k, P4}-free graphs. We prove that if r ≥ 1 and k ≥ 2, and if G is ...