Author
Hansjoachim Walther
Bio: Hansjoachim Walther is an academic researcher. The author has contributed to research in topics: Planar graph & Topology (electrical circuits). The author has an hindex of 3, co-authored 3 publications receiving 165 citations.
Papers
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TL;DR: Knowing estimates of the maximal length of simple circuits in certain 3-connected planar graphs are surveyed and improved in several directions.
107 citations
TL;DR: In this paper, Gallai et al. describe a scenario in which a 3-fach zusammenhangender graph G (bzw. einfach ZSGA H ) is konstruiert, der keinen Knotenpunkt besitzt, durch den alle langsten Wege des Graphen gehen.
56 citations
TL;DR: In this paper, a zweifach zusammenhangender (nichtplanarer) Graph angegeben, der keine zwei Knotenpunkte besitzt, so das jeder langste Kreis des Graphen durch weinigstens einen der beiden Knotenpointte geht.
9 citations
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TL;DR: In this paper, it was shown that every planar graph has an acyclic coloring with nine colors, provided that no circuit is bichromatic, and conjecture that five colors are sufficient.
Abstract: A coloring of the vertices of a graph byk colors is called acyclic provided that no circuit is bichromatic. We prove that every planar graph has an acyclic coloring with nine colors, and conjecture that five colors are sufficient. Other results on related types of colorings are also obtained; some of them generalize known facts about “point-arboricity”.
387 citations
168 citations
TL;DR: This survey has attempted to bring together most of the results and papers that deal with toughness related to cycle structure into a few self explanatory categories.
Abstract: In this survey we have attempted to bring together most of the results and papers that deal with toughness related to cycle structure. We begin with a brief introduction and a section on terminology and notation, and then try to organize the work into a few self explanatory categories. These categories are circumference, the disproof of the 2-tough conjecture, factors, special graph classes, computational complexity, and miscellaneous results as they relate to toughness. We complete the survey with some tough open problems!
127 citations
70 citations
TL;DR: It is proved that every finite group G has a generating set of size at most log"2|G|, such that the corresponding Cayley graph contains a Hamiltonian cycle.
66 citations