Degree sums and subpancyclicity in line graphs

A graph is called subpancyclic if it contains a cycle of length k for each k between 3 and the circumference of the graph. In this paper, we show that if the degree sum of the vertices along each 2-path of a graph G exceeds (n+6)/2, or if the degree sum of the vertices along each 3-path of G exceeds (2n+16)/3, then its line graph L(G) is subpancyclic. Simple examples show that these bounds are best possible. Our results shed some light on the content of a famous Metaconjecture of Bondy

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Subpancyclicity of line graphs and degree sums along paths

A graph is called subpancyclic if it contains a cycle of length $\ell$ for each $\ell$ between 3 and the circumference of the graph. We show that if $G$ is a connected graph on $n\ge 146$ vertices such that $d(u)+d(v)+d(x)+d(y)>(n+10/2)$ for all four vertices $u,v,x,y$ of any path $P=uvxy$ in $G$, then the line graph $L(G)$ is subpancyclic, unless $G$ is isomorphic to an exceptional graph. Moreover, we show that this result is best possible, even under the assumption that $L(G)$ is hamiltonian. This improves earlier sufficient conditions by a multiplicative factor rather than an additive constant