Die Theorie der regulären graphs

  title={Die Theorie der regul{\"a}ren graphs},
  author={Julius Petersen},
  journal={Acta Mathematica},
  • J. Petersen
  • Published 1 December 1891
  • Mathematics
  • Acta Mathematica

Vizing's and Shannon's Theorems for defective edge colouring

We call a multigraph (k, d)-edge colourable if its edge set can be partitioned into k subgraphs of maximum degree at most d and denote as χ d (G) the minimum k such that G is (k, d)-edge colourable.

Regular Colorings in Regular Graphs

This paper completely characterize all 4-regular pseudographs (graphs that may contain parallel edges and loops) which do not have a (3, 1)-coloring.

Graphs with few Hamiltonian Cycles

An algorithm for the exhaustive generation of non-isomorphic graphs with a given number k ≥ 0 of hamiltonian cycles is described, which is especially efficient for small k, and the maximum size of graphs containing exactly one hamiltonia path is determined.

An equivalent formulation of the Fan-Raspaud Conjecture and related problems

This paper answers a question recently proposed by Mkrtchyan and Vardanyan, by giving an equivalent formulation of the Fan-Raspaud Conjecture, and proves it for graphs having oddness at most four and gives a natural extension to bridgeless cubic multigraphs and to certain cubic graphs having bridges.

On Non‐Hamiltonian Graphs for which every Vertex‐Deleted Subgraph Is Traceable

A sharp lower bound on the size of a platypus depending on its order is given, connections to other families of graphs are drawn, and two open problems of Wiener are solved.

On the volume conjecture for classical spin networks

We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they

Highly edge‐connected factors using given lists on degrees

Let G be a 2k‐edge‐connected graph with k≥0 and let L(v)⊆{k,…,dG(v)} for every v∈V(G) . A spanning subgraph F of G is called an L‐factor, if dF(v)∈L(v) for every v∈V(G) . In this article, we show

Derangement action digraphs and graphs

1-Factorizations of Pseudorandom Graphs

  • Asaf FerberVishesh Jain
  • Mathematics, Computer Science
    2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2018
It is proved that for any ε > 0, an (n, d,λ)-graph G (that is, a d-regular graph on n vertices whose second largest eigenvalue in absolute value is at most λ) admits a 1-factorization provided that n is even, and C_0 ≤ d ≤ n-1 (where C-0=C_0(ε) is a constant depending only on ε).