Machine-checked certificates for Haugland's 2131-vertex Moser-spindle-free 5-chromatic unit-distance graph, and a certified reduction to 1501 vertices
{"Haugland":[0],"(arXiv:2608.04542)":[1],"constructed":[2],"a":[3,19,30,93,105,134,148,215,242,253,267,272,313],"unit-distance":[4,77,245],"graph":[5,37,223,246,332],"G₃":[6,84,96,100],"in":[7,57,109,226],"the":[8,51,54,71,75,80,112,123,142,165,191,206,221,263,300,323,330],"plane":[9],"with":[10,133,147,275],"2131":[11],"vertices":[12,187,203,249,257],"that":[13],"contains":[14,85],"no":[15,44,86],"Moser":[16,87],"spindle":[17,88],"as":[18,214],"subgraph":[20],"and":[21,64,99,184,194,201,250,304,312,319,336],"has":[22],"chromatic":[23],"number":[24],"5.":[25],"The":[26,307],"5-chromaticity":[27],"rests":[28],"on":[29,79,171,199,220,247],"SAT":[31],"computation":[32],"for":[33,42,68,266,329],"an":[34],"auxiliary":[35,222],"740-vertex":[36],"G₁":[38,189],"(the":[39],"\\"pair":[40],"property\\"),":[41],"which":[43,110],"proof":[45,136],"artifact":[46],"was":[47,231],"published.":[48],"We":[49,174],"reconstruct":[50],"construction":[52],"from":[53,188,233,260,338],"paper's":[55],"definitions":[56],"exact":[58,81],"cyclotomic":[59],"arithmetic":[60],"(all":[61],"counts":[62],"match),":[63],"give":[65],"machine-checkable":[66],"certificates":[67,311],"every":[69,297],"step:":[70],"edge":[72],"lists":[73],"are":[74,316],"complete":[76],"graphs":[78,198],"point":[82],"sets;":[83],"(a":[89],"DRAT-certified":[90],"refutation":[91],"of":[92,115,182,209,255,299,326],"subgraph-containment":[94],"encoding);":[95],"is":[97,101,117,289,302],"5-colourable;":[98],"not":[102,157],"4-colourable,":[103],"via":[104],"three-part":[106],"chain":[107,301],"L1–L3":[108],"L1,":[111],"pair":[113,192],"property":[114,193],"G₁,":[116],"certified":[118,180,227,303],"by":[119,131,141,285],"cube-and-conquer:":[120],"march_cu":[121],"splits":[122],"instance":[124],"into":[125],"14":[126,172],"786":[127],"cubes,":[128,309],"each":[129],"refuted":[130,284],"kissat":[132],"drat-trim-verified":[135],"(5":[137],"%":[138],"also":[139,175],"checked":[140],"formally":[143],"verified":[144,149],"cake_lpr),":[145],"together":[146],"cover":[150],"certificate.":[151],"Twenty-two":[152],"plain":[153],"CDCL":[154],"configurations":[155],"did":[156],"settle":[158],"L1":[159],"within":[160],"30":[161,183,210,234],"minutes":[162,170],"each,":[163],"whereas":[164],"cube-and-conquer":[166],"campaign":[167,219,264],"took":[168],"16":[169],"cores.":[173],"report":[176],"reduction":[177,254],"experiments.":[178],"Deleting":[179],"sets":[181],"then":[185],"60":[186],"preserves":[190],"yields":[195],"Moser-spindle-free":[196,243],"5-chromatic":[197,244],"2011":[200],"1891":[202],"respectively,":[204],"while":[205],"next":[207],"batch":[208],"cannot":[211],"be":[212,334],"removed":[213],"whole.":[216],"A":[217],"longer":[218],"G₂,":[224],"run":[225],"batches":[228,279],"whose":[229],"size":[230,282],"reduced":[232],"to":[235,237,239],"20":[236],"10":[238],"5,":[240],"reaches":[241],"1501":[248],"8088":[251],"edges,":[252],"630":[256],"(29.6":[258],"%)":[259],"Haugland's":[261],"graph;":[262],"stops":[265],"structural":[268],"reason":[269],"rather":[270,340],"than":[271,292,341],"budget":[273],"one,":[274],"both":[276],"independent":[277],"candidate":[278],"at":[280],"step":[281,298],"5":[283],"explicit":[286],"4-colourings.":[287],"This":[288],"still":[290],"larger":[291],"Heule's":[293],"1441-vertex":[294],"example,":[295],"but":[296],"independently":[305],"re-checkable.":[306],"inputs,":[308],"top-level":[310],"re-verification":[314],"script":[315],"released":[317],"(GitHub":[318],"Zenodo,":[320],"DOI":[321],"10.5281/zenodo.22435777);":[322],"128":[324],"GB":[325],"leaf":[327],"proofs":[328],"1501-vertex":[331],"can":[333],"regenerated":[335],"re-checked":[337],"these":[339],"being":[342],"deposited.":[343]}
Authors
- King Tat Wong (ORCID: https://orcid.org/0009-0003-4009-3619)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-21
- DOI
- https://doi.org/10.5281/zenodo.22878890
- Primary Topic
- Advanced Graph Theory Research
- Type
- preprint