{"ok":true,"nota":{"id":"2b1b27e3f1427847","slug":"matematicos-encuentran-un-grafo-de-228-vertices-que-necesita-cinco-col-2b1b27","titulo":"Matemáticos encuentran un grafo de 228 vértices que necesita cinco colores en una esfera","resumen":"Los autores construyen dos grafos de distancia unitaria sobre una esfera específica que necesitan cinco colores para ser coloreados. Presentan certificados exactos de sus cálculos y los comparan con un antecedente de 372 vértices.","fuente":"zenodo","fuenteNombre":"Zenodo · Investigación abierta","color":"#1682d4","autor":"Crocker, Carson","url":"https://doi.org/10.5281/zenodo.23241819","imagen":"/hoy/portada/2b1b27e3f1427847","tema":"ciencia","subtemas":["teoría de grafos","coloreo","geometría","matemática discreta","icosaedro"],"entidades":["Voronov","Neopryatnaya","Dergachev","Discrete Mathematics"],"formato":"dato","entretenimiento":false,"pubTs":"2026-10-25T06:06:25.000Z","indexTs":"2026-10-27T01:00:26.555Z","hash":"a018d6db2a9e1800e449c8f7d3424b317b987ee670df3c8d5c081ab34f42b57f","tsa":{"time":"Oct 27 01:01:05 2026 GMT","provider":"freetsa.org","sobre":"sello"},"stats":{"views":0,"likes":0,"clicks":0,"dwell":0},"tipo":"normal","registro":"hallazgo","porQueImporta":"Es un problema de matemática pura: cuántos colores hacen falta para pintar puntos de una esfera sin que dos puntos a distancia exacta compartan color. Se trata de avances minuciosos, con 228 vértices frente a los 372 del antecedente. Para la vida cotidiana no cambia nada inmediato, pero este tipo de problemas alimenta la lógica que luego sostiene algoritmos y criptografía. La matemática avanza así, con pasos chicos que nadie aplaude en la calle. Lo que se gana es un récord más preciso sobre algo que el resto del mundo casi no ve.","quienFirma":"Zenodo (institución principal no identificada en el registro)","confianza":"preprint","consulta":null},"sello":{"hash":"a018d6db2a9e1800e449c8f7d3424b317b987ee670df3c8d5c081ab34f42b57f","sello":"63c829a0399929be76abfbbcfe97aa8ead048a8ec5685eadea8a5b3a07360a1b","beacon":{"drand":{"cadena":"8990e7a9aaed2ffed73dbd7092123d6f289930540d7651336225dc172e51b2ce","ronda":6587728,"aleatorio":"5c084ccd88a388daf1762d849f95d0124aca7a6eba6dcadc9bc02bde63b53cf9","tiempo":"2026-10-27T01:01:00.000Z"},"nist":{"cadena":2,"pulso":2001057,"salida":"5B99AC65807BB33F682F0FE1E3937EAABEC5EEF52E18CAFDF2E49A3034ED9A3BCF398EC72E537DE4438FFE76C73678ECEB2D27695900A2EE8B65081177AD66A4","tiempo":"2026-10-27T01:00:00.000Z"},"noAntes":"2026-10-27T01:01:00.000Z"},"verificacion":{"drand":true,"nist":true},"tsa":{"time":"Oct 27 01:01:05 2026 GMT","provider":"freetsa.org","sobre":"sello"},"original":{"titulo":"A 228-vertex 5-chromatic unit-distance graph on the sphere of radius cos(π/10), with exact certificates","descripcion":"<p>This deposit gives two unit-distance graphs on the sphere of radius r = cos(&pi;/10), with r&sup2; = (5+&radic;5)/8. This radius is the circumradius of the icosahedron with unit edges. Each graph has chromatic number 5 and is vertex-critical:</p> <ul> <li>228 vertices and 910 edges;</li> <li>231 vertices and 924 edges.</li> </ul> <p>The graphs are faithful: two points are adjacent exactly when their chord is 1. Voronov, Neopryatnaya and Dergachev constructed a 372-vertex 5-chromatic unit-distance graph on this sphere and noted that it remains 5-chromatic after deletion of any single vertex (Discrete Mathematics 345 (2022), 113106).</p> <p><strong>Construction.</strong> Start from two rotated copies of the icosahedron. Repeatedly add the points at chord 1 from two existing points, then select small 5-chromatic subgraphs. All coordinates lie in a number field of degree 8.</p> <p><strong","pubDate":"2026-10-25T06:06:25Z","url":"https://doi.org/10.5281/zenodo.23241819"},"indexado":"2026-10-27T01:00:26.555Z"}}