31:["$","span","6",{"children":" versus the wheel is not yet explored due to the bit more structural complexity of "}] 4e:T488,

\mathbb{K}_{2,n}

32:["$","span","7",{"dangerouslySetInnerHTML":{"__html":"$4e"}}] 33:["$","span","8",{"children":" compared to the star. In this article, we have established an exact value of "}] 4f:T488,

\mathbb{K}_{2,n}

34:["$","span","9",{"dangerouslySetInnerHTML":{"__html":"$4f"}}] 35:["$","span","10",{"children":" versus "}] 50:T40f,

W_{m}

36:["$","span","11",{"dangerouslySetInnerHTML":{"__html":"$50"}}] 37:["$","span","12",{"children":" for large "}] 38:["$","span","13",{"dangerouslySetInnerHTML":{"__html":"

n

"}}] 39:["$","span","14",{"children":" and "}] 3a:["$","span","15",{"dangerouslySetInnerHTML":{"__html":"

m

"}}] 3b:["$","span","16",{"children":". In particular, we have proved equation* R(K₂,n, W_m)=3n+4, equation* whenever "}] 3c:["$","span","17",{"dangerouslySetInnerHTML":{"__html":"

n

"}}] 3d:["$","span","18",{"children":" and "}] 3e:["$","span","19",{"dangerouslySetInnerHTML":{"__html":"

m

"}}] 3f:["$","span","20",{"children":" are sufficiently large integers satisfying "}] 40:["$","span","21",{"dangerouslySetInnerHTML":{"__html":"

n\\geq4m

"}}] 41:["$","span","22",{"children":" and "}] 42:["$","span","23",{"dangerouslySetInnerHTML":{"__html":"

m

"}}] 43:["$","span","24",{"children":" is an odd integer. This proves the "}] 51:T40f,

W_{m}

44:["$","span","25",{"dangerouslySetInnerHTML":{"__html":"$51"}}] 45:["$","span","26",{"children":"-goodness of "}] 52:T488,

\mathbb{K}_{2,n}

46:["$","span","27",{"dangerouslySetInnerHTML":{"__html":"$52"}}] 47:["$","span","28",{"children":". Our proof combines probabilistic methods with an analysis of structural dependencies. As part of the argument, we resolve a structural rigidity question concerning highly dependent neighbourhoods (Lemma 3.12)."}] 48:["$","div",null,{"className":"flex items-center justify-between gap-3","children":[["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted h-3 w-24"}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted h-3 w-16"}]]}] 49:["$","div",null,{"className":"space-y-2","children":[["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted w-full h-4"}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted w-4/5 h-4"}]]}] 4a:["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted h-3 w-2/3"}] 4b:["$","div",null,{"className":"mt-auto flex gap-2 pt-1","children":[["$","div",null,{"data-slot":"skeleton","className":"animate-pulse bg-muted h-5 w-20 rounded-full"}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse bg-muted h-5 w-16 rounded-full"}]]}] 4c:["$","div","3",{"data-slot":"card","data-size":"default","className":"group/card flex flex-col gap-(--card-spacing) overflow-hidden rounded-xl py-(--card-spacing) text-sm text-card-foreground ring-1 ring-foreground/10 [--card-spacing:--spacing(4)] has-data-[slot=card-footer]:pb-0 has-[>img:first-child]:pt-0 data-[size=sm]:[--card-spacing:--spacing(3)] data-[size=sm]:has-data-[slot=card-footer]:pb-0 *:[img:first-child]:rounded-t-xl *:[img:last-child]:rounded-b-xl relative h-full bg-card/80","children":["$","div",null,{"data-slot":"card-content","className":"relative flex h-full flex-col gap-3 px-5","children":[["$","div",null,{"className":"flex items-center justify-between gap-3","children":[["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted h-3 w-24"}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted h-3 w-16"}]]}],["$","div",null,{"className":"space-y-2","children":[["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted w-full h-4"}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted w-4/5 h-4"}]]}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse rounded-md bg-muted h-3 w-2/3"}],null,["$","div",null,{"className":"mt-auto flex gap-2 pt-1","children":[["$","div",null,{"data-slot":"skeleton","className":"animate-pulse bg-muted h-5 w-20 rounded-full"}],["$","div",null,{"data-slot":"skeleton","className":"animate-pulse bg-muted h-5 w-16 rounded-full"}]]}]]}]}]

Nearby in the stack

Nearby in the stack