Abstract
A Weight graph is a connected (multi)graph with two vertices u and v of degree at least three and other vertices of degree two. Moreover, if any of these two vertices is removed, the remaining graph contains a cycle. A Weight graph is called simple if the degree of u and v is three. We show full computational complexity characterization of the problem of deciding the existence of a locally injective homomorphism from an input graph G to any fixed simple Weight graph by identifying some polynomial cases and some NP-complete cases.
Supported by Charles University as GAUK 95710 and by the grant SVV-2010-261313 (Discrete Methods and Algorithms).
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Bílka, O., Lidický, B., Tesař, M. (2011). Locally Injective Homomorphism to the Simple Weight Graphs. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_46
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DOI: https://doi.org/10.1007/978-3-642-20877-5_46
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