
Congressus Numerantium
ISSN: 0384-9864
Established in 1970, Congressus Numerantium is one of the oldest international journals with a focus on publishing high-quality papers in combinatorics and related areas. Over the years, it has published numerous fully refereed regular papers and conference proceedings for many prestigious conferences. However, publication was temporarily paused on January 15, 2020. Throughout its active years, Congressus Numerantium adopted a print format, following a subscription-based model for readers and releasing 234 Volumes. Despite the changing landscape of academic publishing, Congressus Numerantium demonstrated resilience. In 2024, the journal embarked on a transformative journey, reemerging in both print and online formats with the objective of publishing 2 volumes annually, scheduled for release in June and December. We cordially invite original research papers and survey articles, welcoming significant contributions to both the pure and applied aspects of combinatorics. Furthermore, we extend a warm invitation for special issues dedicated to conferences and workshops in combinatorics and related fields, carrying forward the rich tradition of this esteemed journal. Special issues on selected topics of current interest to the community of combinatorics are also welcome.
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 165-174
- Published: 31/12/2019
Strongly regular graphs with parameters
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 151-164
- Published: 31/12/2019
The game of Nim is at least centuries old, possibly
originating in China, but noted in the 16th century
in European countries. It consists of several stacks
of tokens, and two players alternate taking one or
more tokens from one of the stacks, and the player
who cannot make a move loses.
The formal and intense study of Nim culminated in
the celebrated Sprague-Grundy Theorem, which is now
one of the centerpieces in the theory of impartial
combinatorial games.
We study a variation on Nim, played on a graph. Graph Nim, for which the theory of
Sprague-Grundy does not provide a clear strategy.
Graph Nim was originally developed at the University
of Colorado Denver.
Graph Nim was first played on graphs of three
vertices. The winning strategy and losing position
of three-vertex Graph Nim have been discovered,
but we will expand the game to four vertices and
develop the winning strategies for four-vertex
Graph Nim.
This work was published as a chapter in the
Master’s Thesis of Trevor Williams [8].
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 143-150
- Published: 31/12/2019
This article discusses Kirchhoff graph uniformity—that all edge vectors in a Kirchhoff graph have the same multiplicity. For a given Kirchhoff graph, an associated digraph is constructed. Based on these graphs, the equivalence of a linear-algebraic condition and a vector graph being Kirchhoff is proven. This condition is then used to show that
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 125-142
- Published: 31/12/2019
Consider the following two-person game on a graph
The advantage of the game proper chromatic number is that it is comparable to other published game chromatic variants, particularly the game chromatic number II and the game Grundy number.
This paper also considers extensions of the game proper chromatic number through generalized regions of the graph. Let
The minimum number of colors necessary provided each player plays optimally, following the rules established for the game proper chromatic number, is denoted
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 119-124
- Published: 31/12/2019
A conjecture by Albertson states that if
In this paper, we consider the statements corresponding to this conjecture where the crossing number of
– the genus
– the skewness
– the thickness
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 111-118
- Published: 31/12/2019
In 2017, Hedetniemi asked the question: “For which graphs
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 103-110
- Published: 31/12/2019
We give necessary and sufficient conditions for two matroids on the same ground set to be the upper and lower matroids of a
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 95-102
- Published: 31/12/2019
Let
A cycle
A digraph is 1,2-cycle-extendable if every non-Hamiltonian cycle is either 1-extendable or 2-extendable. It has been previously shown that not all strong tournaments (orientations of a complete undirected graph) are 1-extendable, but are 2-extendable. The structure of all non 1-extendable tournaments is shown as a type of block Kronecker product of 1-extendable subtournaments.
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 79-94
For a toroidal graph
Let
We say that a
We determine all antipodal balanced
- Research article
- Full Text
- Congressus Numerantium
- Volume 233
- Pages: 53-78
- Published: 31/12/2019
Steinhaus graphs are a small (there are
In this paper, we find and count all the complements of Steinhaus graphs that are claw-free.