# The Julius Petersen Graph Theory Centennial

## 1st Edition

**Editors:**L.D. Andersen J. Bang-Jensen T.R. Jensen L.K. Jørgensen G. Sabidussi C. Thomassen B. Toft P.D. Vestergaard

**eBook ISBN:**9781483296326

**Imprint:**North Holland

**Published Date:**8th October 1992

**View all volumes in this series:**Topics in Discrete Mathematics

## Table of Contents

Problems worthy of attack (P. Hein). Julius Petersen Photographs. Julius Petersen 1839-1910, A biography (J. Lützen, G. Sabidussi, B. Toft). Julius Petersen annotated bibliography (M. Christiansen et al.). Correspondence between Sylvester, Petersen, Hilbert and Klein on invariants and the factorisation of graphs 1889-1891 (G. Sabidussi). Julius Petersen's theory of regular graphs (H.M. Mulder). Matching theory - a sampler: from Dénes König to the present (M.D. Plummer). We shall have to evolve (P. Hein). On a conjecture of Gallai concerning complete subgraphs of *k*-critical graphs (H.L. Abbott, B. Zhou). On total covers of graphs (Y. Alavi et al.). Turán theorems with repeated degrees (M.O. Albertson). On the structure of locally semicomplete digraphs (J. Bang-Jensen). Precoloring extension. l. interval graphs (M. Biró, M. Hujter, Z. Tuza). Cyclic coloring of plane graphs (O.V. Borodin). Determinants and current flows in electric networks (R.L. Brooks et al.). The ubiquitous Petersen graph (G. Chartrand, H. Hevia, R.J. Wilson). The end structure of a graph: recent results and open problems (R. Diestel). Coflow polyhedra (K. Cameron, J. Edmonds). Extremal problems involving vertices and edges on odd cycles (P. Erdős, R.J. Faudree, C.C. Rousseau). Spanning Eulerian subgraphs, the Splitting Lemma, and Petersen's Theorem (H. Fleischner). A solution to a colouring problem of P. Erdős (H. Fleischner, M. Stiebitz). On a theorem of Mader (A. Frank). Indecomposable regular graphs and hypergraphs (Z. Füredi). On the r-domination number of a
graph (J.R. Griggs, J.P. Hutchinson). Enumeration of regular graphs 100 years ago (H. Gropp). The Cartesian product of a *k*-extendable and an l-extendable graph is (k + l + 1)-extendable (E. Györi, M.D. Plummer). Some finiteness results concerning separation in graphs (R. Halin). A quick proof that K10≠P+P+P (D. Hanson). On cages with given degree sets (D. Hanson, P. Wang, L.K. Jørgensen). On 3-connected graphs with contractible edge covers of size *k* (R.L. Hemminger, X. Yu). The chromatic index of a graph whose core has maximum degree two (A.J.W. Hilton, Z. Cheng). A new invariant of plane bipartite cubic graphs (F. Jaeger). Colorful induced subgraphs (H.A. Kierstead, W.T. Trotter). An extension of the multi-path algorithm for finding hamilton cycles (W. Kocay). List edge chromatic number of graphs with large girth (A.V. Kostochka). *T*-colorings of graphs (D.D.-F. Liu). Conjecture de Hadwiger: *k*=6.II-Réductions de sommets de degré 6 dans les graphes 6-chromatiques contraction-critiques (J. Mayer). On Ramsey graphs without bipartite subgraphs (J. Nešetřil, V. Rödl). Plurality preference digraphs realized by trees, II: On realization numbers (K.B. Reid, W. Gu). Binary invariants and orientations of graphs (G. Sabidussi). How to calculate the number of perfect matchings in finite sections of certain infinite plane graphs (H. Sachs). Cycles of length 2 modulo 3 in graphs (A. Saito). Hajós' conjecture and small cycle double covers of planar graphs (K. Seyffarth). On Hadwiger's number-A problem of the Nordhaus-Gaddum type (M. Stiebitz). Cycles containing many vertices of large degree (H.J. Veldman). An inequality for chromatic polynomials (D.R. Woodall). A zero-free interval for chromatic polynomials (D.R. Woodall). Gallai's problem on Dirac's construction (D.A. Youngs). Unsolved problems presented at the Julius Petersen Graph Theory Conference (J. Bang-Jensen, B. Toft). The road to wisdom? (P. Hein).

## Description

Julius Petersen's paper, Die Theorie der regulären graphs in *Acta Mathematica*, volume 15 (1891), stands at the beginning of graph theory as we know it today.

The Danish group of graph theorists decided in 1985 to mark the 150th birthday of Petersen in 1989, as well as the centennial of his paper.

It was felt that the occasion called for a presentation of Petersen's famous paper in its historical context and, in a wider sense, of Petersen's life and work as a whole. However, the readily available information about Julius Petersen amounted to very little (not even a full bibliography existed) and virtually nothing was known about the circumstances that led him to write his famous paper.

The study of Petersen's life and work has resulted in several papers, in particular a biography, a bibliography, an annotated edition of the letters surrounding Petersen's paper of 1891, an analysis of Petersen's paper and an annotated edition of parts of Petersen's correspondence with Sylow on Galois theory. The first four of these papers, together with a survey of matching theory, form the first part of this book. In addition to these five special papers, there are papers submitted in the celebration of the Petersen centennial.

## Details

- Language:
- English

- Copyright:
- © North Holland 1992

- Published:
- 8th October 1992

- Imprint:
- North Holland

- eBook ISBN:
- 9781483296326

## Reviews

@qu:This is simply an excellent book which no graph theorist should miss... @source:European Mathematical Society Newsletter