
Ars Combinatoria
ISSN 0381-7032 (print), 2817-5204 (online)
Ars Combinatoria is the oldest Canadian Journal of Combinatorics, established in 1976. The journal is dedicated to advancing the field of combinatorial mathematics through the publication of high-quality research papers. From 2024 onward, it publishes four volumes per year in March, June, September and December. Ars Combinatoria has gained recognition and visibility in the academic community and is indexed in renowned databases such as MathSciNet, Zentralblatt, and Scopus. The Scope of the journal includes Graph theory, Design theory, Extremal combinatorics, Enumeration, Algebraic combinatorics, Combinatorial optimization, Ramsey theory, Automorphism groups, Coding theory, Finite geometries, Chemical graph theory but not limited.
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- Research article
- Full Text
- Ars Combinatoria
- Volume 084
- Pages: 33-49
- Published: 31/07/2007
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 084
- Pages: 23-31
- Published: 31/07/2007
In this paper, we consider a certain second order linear recurrence and then give generating matriees for the sums of positively and negatively subscripted terms of this recurrence. Further, we use matrix methods and derive explicit. formulas for these sums.
- Research article
- Full Text
- Ars Combinatoria
- Volume 084
- Pages: 13-22
- Published: 31/07/2007
For a simple and finite graph \(G = (V,E)\), let \(w_{\max}(G)\) be the maximum total weight \(w(E) = \sum_{e\in E} w(e)\) of \(G\) over all weight functions \(w: E \to \{-1,1\}\) such that \(G\) has no positive cut, i.e., all cuts \(C\) satisfy \(w(C) \leq 0\).
For \(r \geq 1\), we prove that \(w_{\max}(G) \leq -\frac{|V|}{2}\) if \(G\) is \((2r-1)\)-regular and \(w_{\max}(G) \leq -\frac{r|V|}{2r+1}\) if \(G\) is \(2r\)-regular. We conjecture the existence of a constant \(c\) such that \(w_{\max}(G) \leq -\frac{5|V|}{6} + c\) if \(G\) is a connected cubic graph and prove a special case of this conjecture. Furthermore, as a weakened version of this conjecture, we prove that \(w_{\max}(G) \leq -\frac{2|V|}{3}+\frac{2}{3}\) if \(G\) is a connected cubic graph.
- Research article
- Full Text
- Ars Combinatoria
- Volume 084
- Pages: 3-11
- Published: 31/07/2007
Let \(G_i\) be the subgraph of \(G\) whose edges are in the \(i\)-th color in an \(r\)-coloring of the edges of \(G\). If there exists an \(r\)-coloring of the edges of \(G\) such that \(H_i \nsubseteq G_i\) for all \(1 \leq i \leq r\), then \(G\) is said to be \(r\)-colorable to \((H_1, H_2, \ldots, H_r)\). The multicolor Ramsey number \(R(H_1, H_2, \ldots, H_r)\) is the smallest integer \(n\) such that \(K_n\) is not \(r\)-colorable to \((H_1, H_2, \ldots, H_r)\). It is well known that \(R(C_m, C_4, C_4) = m + 2\) for sufficiently large \(m\). In this paper, we determine the values of \(R(C_m, C_4, C_4)\) for \(m \geq 5\), which show that \(R(C_m, C_4, C_4) = m + 2\) for \(m \geq 11\).
- Research article
- Full Text
- Ars Combinatoria
- Volume 083
- Pages: 381
- Published: 30/04/2007
The proof of gracefulness for the Generalised Petersen Graph \(P_{8t,3}\) for every \(t \geq 1\), written by the same author (Graceful labellings for an infinite class of generalised Petersen graphs, Ars Combinatoria \(81 (2006)\), pp. \(247-255)\), requires the change of just one label, for the only case \(t = 5\).
- Research article
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- Ars Combinatoria
- Volume 083
- Pages: 365-379
- Published: 30/04/2007
For words of length \(n\), generated by independent geometric random variables, we study the average initial and end heights of the last descent in the word. In addition, we compute the average initial and end height of the last descent in a random permutation of \(n\) letters.
- Research article
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- Ars Combinatoria
- Volume 083
- Pages: 361-363
- Published: 30/04/2007
We construct a record-breaking binary code of length \(17\), minimal distance \(6\), constant weight \(6\), and containing \(113\) codewords.
- Research article
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- Ars Combinatoria
- Volume 083
- Pages: 353-359
- Published: 30/04/2007
The purpose of this note is to give the power formula of the generalized Lah matrix and show \(\mathcal{L}[x,y] = \mathcal{FQ}[x,y]\), where \(\mathcal{F}\) is the Fibonacci matrix and \(\mathcal{Q}[x,y]\) is the lower triangular matrix. From it, several combinatorial identities involving the Fibonacci numbers are obtained.
- Research article
- Full Text
- Ars Combinatoria
- Volume 083
- Pages: 341-352
- Published: 30/04/2007
A graph is called set reconstructible if it is determined uniquely (up to isomorphism) by the set of its vertex-deleted subgraphs. We prove that some classes of separable graphs with a unique endvertex are set reconstructible and show that all graphs are set reconstructible if all \(2\)-connected graphs are set reconstructible.
- Research article
- Full Text
- Ars Combinatoria
- Volume 083
- Pages: 335-339
- Published: 30/04/2007
We prove the following extension of the Erdős-Ginzburg-Ziv Theorem. Let \(m\) be a positive integer. For every sequence \(\{a_i\}_{i\in I}\) of elements from the cyclic group \(\mathbb{Z}_m\), where \(|I| = 4m – 5\) (where \(|I| = 4m – 3\)), there exist two subsets \(A, B \subseteq I\) such that \(|A \cap B| = 2\) (such that \(|A \cap B| = 1\)), \(|A| = |B| = m\), and \(\sum\limits_{i\in b} a_i = \sum\limits_{i\in b} b_i = 0\).