Let T be a topos. Let Ki = [Ai ui → Bi] (for i = 1, 2, 3) be a complex of commutative groups of T with Ai in degree 1 and Bi in degree 0. We define the geometrical notions of extension of K1 by K3 and of biextension of (K1, K2) by K3. These two notions generalize to complexes with two entries the classical notions of extension and biextension of commutative groups of T. We then apply the geomet...

In this paper, we characterize the degree sequences excluding a square in terms of forcibly chordal graphs.

F. Cukierman asked whether or not for every smooth real plane curve X ⊂ P of even degree d > 2 there exists a real line L ⊂ P such X ∩ L has no real points. We show that the answer is “yes” if d = 2 or 4 and “no” if n > 6.

A sequence S is potentially Km − H-graphical if it has a realization containing a Km − H as a subgraph. Let σ(Km − H,n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Km−H,n) is potentially Km−H-graphical. In this paper, we determine σ(Kr+1−(kP2 ⋃ tK2), n) for n ≥ 4r+10, r+1 ≥ 3k+2t, k+t ≥ 2, k ≥ 1, t ≥ 0 .

In [3], Bodlaender and Engelfriet proved that for every k, and d, there exists a constant ck;d, such that every graph with treewidth at most k and maximum degree at most d has domino treewidth at most ck;d. This note gives a new, simpler proof of this fact, with a much better bound for ck;d, namely (9k + 7)d(d+ 1) 1. It is also shown that a lower bound of (kd) holds: there are graphs with domin...

This paper presents a coupled elastoplastic constitutive model for predicting the hydraulic and stress-strain-strength behaviour of unsaturated soils. Hydraulic hysteresis in the water-retention behaviour is modeled as an elastoplastic process with the elastic region of the saturation degree. The effect of change in degree of saturation on the stress-strain-strength behaviour and the effect of ...

A (d, k) -forest is a forest consisting of trees whose diameters are at most d and whose maximum vertex degree ,6. is at most k. The (d, k)-arboricity of a graph G is the minimum number of (d, k}-forests needed to cover E(G). This concept is a common generalization of linear k-arboricity and star arboricity. Using a probabilistic approach developed recently for linear karboricity, we obtain an ...

It is proved in this paper that every bipartite graphic sequence with the minimum degree δ ≥ 2 has a realization that admits a nowhere-zero 4-flow. This result implies a conjecture originally proposed by Keedwell (1993) and reproposed by Cameron (1999) about simultaneous edgecolorings and critical partial Latin squares. ∗Mathematics Subject Classification (2000): 05C15, 05B15, 05C38, 05C70, 05C07.

A sequence S is potentially Km−C4 graphical if it has a realization containing a Km−C4 as a subgraph. Let σ(Km−C4, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Km−C4, n) is potentially Km−C4 graphical. In this paper, we prove that σ(Km−C4, n) ≥ (2m−6)n−(m−3)(m−2)+2, for n ≥ m ≥ 4. We conjectured that equality holds for n ≥ m ≥ 4. We proved that thi...

Using Rado’s theorem for the existence of an independent transversal of family of subsets of a set on which a matroid is defined, we give a proof of Landau’s theorem for the existence of a tournament with a prescribed degree sequence. A similar approach is used to determine when a partial tournament can be extended to a tournament with a prescribed degree sequence. Mathematics Subject Classific...