Geodesic
Discrete Morse inequalities on infinite graphs
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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The goal of this paper is to extend to infinite graphs the known Morse inequalities for discrete Morse functions proved by R. Forman in the finite case. In order to get this result we shall use a special kind of infinite subgraphs on which a discrete Morse function is monotonous, namely, decreasing rays. In addition, we shall use this result to characterize infinite graphs by the number of critical elements of discrete Morse functions defined on them.
DOI : 10.37236/127
Classification : 05C63, 05C10, 57M15, 57Q15
Mots-clés : infinite graphs, Morse inequalities, Morse functions, infinite subgraphs 
@article{10_37236_127,
     author = {Rafael Ayala and Luis M. Fern\'andez and Jos\'e A. Vilches},
     title = {Discrete {Morse} inequalities on infinite graphs},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/127},
     zbl = {1182.05088},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/127/}
}
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Rafael Ayala; Luis M. Fernández; José A. Vilches. Discrete Morse inequalities on infinite graphs. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/127

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