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Isaak Hieronymus Wolf, M. Sc.

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 Isaak Hieronymus Wolf, M. Sc.

PACE - Paderborn Center for Advanced Studies

Doktorand

Diskrete Mathematik/Graphentheorie

Doktorand

Büro:
F2.220
Besucher:
Fürstenallee 11
33102 Paderborn
 Isaak Hieronymus Wolf, M. Sc.
11/2020

Doktorand

Arbeitsgruppe Diskrete Mathematik / Graphentheorie, Universität Paderborn. Gefördert durch die Deutsche Forschungsgemeinschaft (DFG), grant STE 792/3-1.

04/2017 - 11/2019

Master of Science

Mathematik, Universität zu Köln.

10/2013 - 03/2017

Bachelor of Science

Mathematik, Friedrich-Schiller-Universität Jena.


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2022

Even Factors in Edge-Chromatic-Critical Graphs with a Small Number of Divalent Vertices

E. Steffen, I.H. Wolf, Graphs and Combinatorics (2022), 38(3), 104

DOI


Pairwise disjoint perfect matchings in r-edge-connected r-regular graphs

Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, in: arXiv:2206.10975, 2022

Thomassen [Problem 1 in Factorizing regular graphs, J. Combin. Theory Ser. B, 141 (2020), 343-351] asked whether every r-edge-connected r-regular graph of even order has r−2 pairwise disjoint perfect matchings. We show that this is not the case if r≡2 mod 4. Together with a recent result of Mattiolo and Steffen [Highly edge-connected regular graphs without large factorizable subgraphs, J. Graph Theory, 99 (2022), 107-116] this solves Thomassen's problem for all even r. It turns out that our methods are limited to the even case of Thomassen's problem. We then prove some equivalences of statements on pairwise disjoint perfect matchings in highly edge-connected regular graphs, where the perfect matchings contain or avoid fixed sets of edges. Based on these results we relate statements on pairwise disjoint perfect matchings of 5-edge-connected 5-regular graphs to well-known conjectures for cubic graphs, such as the Fan-Raspaud Conjecture, the Berge-Fulkerson Conjecture and the 5-Cycle Double Cover Conjecture.


Bounds for the chromatic index of signed multigraphs

E. Steffen, I.H. Wolf, in: arXiv:2206.11052, 2022

The paper studies edge-coloring of signed multigraphs and extends classical Theorems of Shannon and König to signed multigraphs. We prove that the chromatic index of a signed multigraph (G,σG) is at most ⌊32Δ(G)⌋. Furthermore, the chromatic index of a balanced signed multigraph (H,σH) is at most Δ(H)+1 and the balanced signed multigraphs with chromatic index Δ(H) are characterized.


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