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Deciding k-Colorability of P5-Free Graphs in Polynomial Time
The problem of computing the chromatic number of a P5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show that for every fixedExpand
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An efficient algorithm for generating necklaces with fixed density
A k-ary necklace is an equivalence class of k-ary strings under rotation. A necklace of fixed density is a necklace where the number of zeros is fixed. We present a fast, simple, recursive algorithmExpand
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Generating Bracelets in Constant Amortized Time
  • J. Sawada
  • Computer Science, Mathematics
  • SIAM J. Comput.
  • 2001
A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (i.e.,Expand
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Constructions of k-critical P5-free graphs
With respect to a hereditary class C of graphs, a k -chromatic graph G ? C is said to be k -critical if every proper subgraph of G belonging to C is k - 1 colorable. It is known that there is aExpand
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A Hamilton Path for the Sigma-Tau Problem
Nijenhuis and Wilf asked the following question in their Combinatorial Algorithms textbook from 1975: Can the permutations of {1, 2,...,n} be ordered so that each permutation is transformed into theExpand
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Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)
Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an equivalence class of k-ary strings underExpand
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A Certifying Algorithm for 3-Colorability of P5-Free Graphs
We provide a certifying algorithm for the problem of deciding whether a P 5-free graph is 3-colorable by showing there are exactly six finite graphs that are P 5-free and not 3-colorable and minimalExpand
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A fast algorithm to generate necklaces with fixed content
  • J. Sawada
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
  • 14 May 2003
We develop a fast algorithm for listing all necklaces with fixed content. By fixed content, we mean the number of occurrences of each alphabet symbol is fixed. Initially, we construct a simple butExpand
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De Bruijn Sequences for Fixed-Weight Binary Strings
De Bruijn sequences are circular strings of length $2^n$ whose length n substrings are the binary strings of length n. Our focus is on creating circular strings of length $\binom{n}{w}$ for theExpand
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On Prefix Normal Words and Prefix Normal Forms
Abstract A 1-prefix normal word is a binary word with the property that no factor has more 1s than the prefix of the same length; a 0-prefix normal word is defined analogously. These words arise inExpand
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