Julius Petersen's theory of regular graphs

نویسنده

  • Henry Martyn Mulder
چکیده

Mulder, H.M., Julius Petersen’s theory of regular graphs, Discrete Mathematics 100 (1992) 157-17s. In 1891 the Danish mathematician Julius Petersen (1839-1910) published a paper on the factorization of regular graphs. This was the first paper in the history of mathematics to contain fundamental results explicitly in graph theory. In this report Petersen’s results are analysed and their development in subsequent decades are followed.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Application of Petersen’s Theorem To Finite Element Triangulations

This letter shows that for every finite element triangulation in R, there exists a coloring where each triangle has exactly one red and two black edges. This result is shown using Petersen’s Theorem which states that all bridgeless 3-regular graphs have a perfect matching. The existence of such a coloring has useful applications when the finite element method is applied to problems with solutio...

متن کامل

Petersen's Theorem

In this lecture we will cover: 1. Topics related to Edmonds-Gallai decompositions ([Sch03], Chapter 24). 2. Factor critical-graphs and ear-decompositions ([Sch03], Chapter 24). Topics mentioned but covered during subsequent lectures are: 1. The matching polytope ([Sch03], Chapter 25). 2. Total Dual Integrality (TDI) and the Cunningham-Marsh formula ([Sch03], Chapter 25). A detailed reference on...

متن کامل

H-E-Super magic decomposition of graphs

An H-magic labeling in an H-decomposable graph G is a bijection f : V (G)∪E(G)→ {1, 2, . . . , p+ q} such that for every copy H in the decomposition, ∑ v∈V (H) f(v)+ ∑ e∈E(H) f(e) is constant. The function f is said to be H-E-super magic if f(E(G)) = {1, 2, . . . , q}. In this paper, we study some basic properties of m-factor-E-super magic labeling and we provide a necessary and sufficient cond...

متن کامل

Graphs with the Circuit Cover Property

A circuit cover of an edge-weighted graph (G, p) is a multiset of circuits in G such that every edge e is contained in exactly p(e) circuits in the multiset. A nonnegative integer valued weight vector p is admissible if the total weight of any edge-cut is even, and no edge has more than half the total weight of any edge-cut containing it. A graph G has the circuit cover property if (G, p) has a...

متن کامل

The vertex primitive and vertex bi-primitive s-arc regular graphs

A complete classification is given of vertex primitive and vertex bi-primitive s-arc regular graphs with s ≥ 3. In particular, it is shown that the Petersen graph and Coxeter graph are the only vertex primitive 3-arc regular graphs, and that vertex bi-primitive 3-arc regular graphs consist of the complete bipartite graph K3,3, the standard double covers of the Petersen graph and Coxeter graph, ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Discrete Mathematics

دوره 100  شماره 

صفحات  -

تاریخ انتشار 1992