An Iterative Approach to the Traceability Conjecture for Oriented Graphs
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Published:2013-03-24
Issue:1
Volume:20
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Van Aardt Susan,Burger Alewyn,Dunbar Jean,Frick Marietjie,Harris John,Singleton Joy
Abstract
A digraph is $k$-traceable if its order is at least $k$ and each of its subdigraphs of order $k$ is traceable. The Traceability Conjecture (TC) states that for $k\geq 2$ every $k$-traceable oriented graph of order at least $2k-1$ is traceable. It has been shown that for $2\leq k\leq 6$, every $k$-traceable oriented graph is traceable. We develop an iterative procedure to extend previous results regarding the TC. In particular, we prove that every $7$-traceable oriented graph of order at least 9 is traceable and every 8-traceable graph of order at least 14 is traceable.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
2 articles.
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