On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs

A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-type conditions) imposing of which on specific induced subgraphs of a 2-connected implicit claw-heavy graph ensures its Hamiltonicity. In particular, we improve a recent result of [X. Huang, Implicit degree condition for Hamiltonicity of 2-heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o-heavy and f-heavy subgraphs for Hamiltonicity of 2-connected graphs

On implicit heavy subgraphs and hamiltonicity of 2–connected graphs

International audienceA graph G of order n is implicit claw–heavy if in every induced copy of K 1,3 in G there are two non–adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore– and Fan–type conditions) imposing of which on specific induced subgraphs of a 2–connected implicit claw–heavy graph ensures its hamiltonicity. In particular, we improve a recent result of [X. Huang, Implicit degree condition for hamiltonic-ity of 2–heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o–heavy and f–heavy sub-graphs for hamiltonicity of 2–connected graphs

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

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum