Problems

It seems likely that this is the only such case, though we do not have a proof yet.

More general: does it hold for all monadic-second order definable problems? We conjecture not

rgirth(F)≤2 ∑_1≤i≤nfrac1|F_i|+1 for any family F=(F_1,...,F_n) of subsets of E(K_n) .

Let h(t) be a polynomial of degree s ≤ d with nonnegative coefficients that satisfies Properties (H) and (S). Does U_r^d+1h(t) have an interlacing symmetric decomposition for all r ≥ d+1 (possibly even for r ≥ maxs, d+1-s)?

In this range the best lattice for Q3 is also a best lattice for Q2, and we conjecture that this is always true.

The ratio generating A130296.

We conjecture that the range of k ∈ N in Lemma 2.6 can be extended to k ∈ R.

Determine the least positive integer k such that β(G)-β_b(G)≤k for any graph G.

We have [x^n]g_m(x)=[x^n](frac-x(1-W(-x))^mW(-x))^n, where g_m(x) is the generating function of the central coefficients (m-2)n+1/(m-1)n+1( cmn ) of the Riordan array (c(x),xc(x)^m-2) .

When is it that χ_{td}(cl(G))=2 χ_{td}(G)+1 ? Are there infinitely many graphs with this property?

The coefficient of q in hatE_k,n(q) is binomnk+1binomnk-2.

they conjectured that C_m × P_n is SEAT if m ≥ 4 even, n ≥ 3 and d ∈ 0, 2;

Does there exist a natural filtration {0=\mathcal{F}{0}\subset \mathcal{F}{1}\subset \cdots } on the ring of semi-invariants SI(Q,\beta) such that for a special quiver Q=T_{n,n,n} and a special dimensional vector \beta , see [14], Section…

In the poset of graphs and cc mappings between them, is every non-degenerate interval nonempty? Does every nondegenerate interval contain an infinite antichain? Does every nondegenerate interval contain every countable poset?

For every r ≥0 and every h≥h0(r), where h0(r) depends on r, there is an integer p1(h,r) depending on h and r, such that for every p≥p1(h,r), each member of K^{-r}(p,p+h) is χ-unique.

Let K_n_1,n_2,...,n_r be a complete r-partite graph with r vertex sets X_i(i ∈[1,r]) and |X_i|=n_i , ∑_i=1^r=n . Besides (i) and (ii) in Theorem 8, fgndi_∑(K_n_1,n_2,...,n_r)≤ 3 ?

Is this true “for any graph G, dis_s[G] ≤ χ(G)?”

For any nonnegative integer k, does there exist a connected graph G satisfying φ_(2,j)(G) − κ_(2,j)(G) + 1 = k?

Is there a graph G such that for any non-empty graph H, we have χ_{td}(H □ G) > χ_{td}(G)?

For any x ∈(-3,c) with x ≠ 0, we have ∑_k=0^∞fracx^3k(k+1)(x-1)^k( c3k k )= frac3(x-1)2x^3log^2(1-x)+frac2(1-x)x^3q(x)^2 +s(x)log(1-x)+fract(x)q(x)√(1-x)(3+x), (1.17) where s(x) and t(x) are suitable rational functions in x.