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If ζ(α) = ζ(β), are α and β necessarily related by switching?

If L_S = 1, then S = \varnothing.

Possibly, however, it holds whenever G succcurlyeq H and H is transitive; this is not hard to verify when H is an edge.

The number of finite non-cyclic self 2-distance graphs with no induced subgraphs isomorphic to a square, a diamond, a complete graph with four vertices, or a butterfly is finite.

Is it true that the edges of any graph G with minimum degree d can be partitioned into pairwise disjoint sets, so that each set forms a spanning star forest of G in which every component is of size at least h(d), where h(d) tends to…

Let G be an edge-colored 2-connected graph on n vertices satisfying Fan's condition (see [9]), i.e., maxd(u), d(v) ≥ n/2 for every pair of vertices u, v of G with dist(u, v) = 2. Can G contain a compatible spanning circuit visiting each…

We further conjecture that an elliptic quadric is incident with m modulo q points of an m-ovoid of Q(4, q).

Determining the inversion polynomial for the permutations that avoid this subset of consecutive patterns remains an open question.

Are the properties of being Hamiltonian and planar complete?

For every regular multigraph G, Y_2(G) = Y(G).

The set E_n is a minimal generating set in the weak sense: no proper subset of E_n generates C_n .

For m, r nonnegative integers, P_(m^r)(q,t)=∑_substackλ ⊂(m^r) 2-core(λ)=0f_λ(q^-m,q^r/T;q,t)tildeK_(m^r)-λ(q,t,T;± q^1/2,± t^1/2) and for m, r, n nonnegative integers such that r \leq n, P_(m^r)(x^±;q,t)=∑_substackλ ⊂(m^r)…

For two integers n ≥ 3 and p ≥ 4, f(hatS_p^n) = p^n - fracp^n-18 + fracp^n-2 + … + p8 + 5p/8, if p is even p^n - fracp^n-1 + p^n-2 - 5p + 38, if p is odd.

The case when k is odd was posed as an open problem by Nikiforov [53].

they conjectured that L_n is SEAT if n ≥ 2 even and d ∈ 0, 2;

Let T be a 3-colored (in general, m-colored) tournament not containing 3-colored directed triangles. Must T contain a vertex v such that for every other vertex x of T there exists x rightsquigarrow_mv ? (Or equivalently, must T have a…

It is not known whether there is a finite k-chromatic graph of girth at least g and with \chi_{c}^{s}(G)=2k.

We conjecture that uniqueness of the MCB implies U ≠ ∅.

Equivalently, what is the com putational complexity of EDGE CLIQUE COVER on C_4 -free graphs?

If n ≥ 8, then each tournament of order n contains a double point.