Geodesic
Word-representable graphs: orientations, posets, and bounds
Zion Hefty1 ; Paul Horn1 ; Colby Muir2 ; Andrew Owens3
1University of Denver
2Auburn University
3Widener University
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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Word-representable graphs were originally introduced by Kitaev and Pyatkin, motivated by work of Kitaev and Seif in algebra. Since their introduction, however, there has been a great deal of work in understanding their graph theoretical properties. In this paper, we introduce tools from partially ordered sets, Ramsey theory as well as probabilistic methods to study them. Through these, we settle a number of open problems in the field, regarding both the existence and length of word-representations for various classes of graphs.
DOI : 10.37236/12806
Classification : 05C62, 06A07, 05C20, 05D10, 60C05
Mots-clés : semi-transitive orientability, chromatic number

Zion Hefty  1   ; Paul Horn  1   ; Colby Muir  2   ; Andrew Owens  3

1 University of Denver
2 Auburn University
3 Widener University 
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     author = {Zion Hefty and Paul Horn and Colby Muir and Andrew Owens},
     title = {Word-representable graphs: orientations, posets, and bounds},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {4},
     doi = {10.37236/12806},
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Zion Hefty; Paul Horn; Colby Muir; Andrew Owens. Word-representable graphs: orientations, posets, and bounds. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12806

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