Showing papers in "Discrete Mathematics in 1988"

TL;DR: This paper constructs explicitly graphs with O(m/@e) vertices and maximum degree O(1/@ e^2), such that after removing any (1-@e%) portion of their vertices or edges, the remaining graph still contains a path of length m.

TL;DR: CNCL deletes those conjectures of the second and third type in which one of the invariants on the left is always smaller than an invariant on the right that may undoubtedly remove a number of interesting conjectures.

TL;DR: This chapter discusses the problems and results that arise in combinatorial analysis and the graph theory, illustrating two recent problems, and states that the main difficulty is perhaps the lack of constructive methods.

TL;DR: This paper shows that both the nonseparating independent set problem and feedback set problem can be solved in polynomial time for graphs with no vertex degree exceeding 3 by reducing the problems to the matroid parity problem.

TL;DR: Generalisation naturelle d'une grande partie de theorie qualitative de la theorie qualitative de Ramsey et caracterisation de certaines structures associees.

TL;DR: The maximum number of maximal independent sets which a connected graph on n vertices can have is determined, and the extremal graphs are completely characterize, thereby answering a question of Wilf.

TL;DR: It is proved that Z ( H ) is a connected bipartite graph if H has at least one perfect matching and that those hexagonal systems whose Z -transformation graphs are not 2-connected are given.

TL;DR: This paper focuses on some results on the following two packing problems: dense packings of trees of different sizes into Kn.

TL;DR: It is proved that a contraction- critical, finite graph G has at least ∣ G ∣/3 triangles and that a finite graphs G is 8-connected if every complete subgraph of G is contained in a smallest separating set of G .

TL;DR: This result is used to inductively construct injections showing the log concavity of the binomial coefficients and Stirling numbers of both kinds, and is related to the graphical interpretation of these numbers given by Wilf.

TL;DR: It is shown that a necessary and sufficient condition for the existence of a P 3 -factorization of K m,n is (i) m + n =0 (mod 3), (ii) m ⩽ 2n, (iii) n 2m and (iv) 3 mn/2(m + n ) is an integar.

TL;DR: It is shown that a subgraph count has the form of an incomplete U-statistics, and asymptotic normality of subgraph counts for a wide range of values of p is proved, including any constant p and sequences of p(n) tending to 0 or 1 sufficiently slowly.

TL;DR: It is shown that i + IR⩽2n + 2δ − 2 2nδ , which was conjectured by Cockayne, Favaron, Payan and Thomason, and that i = i + 2 δIR ⩽n + δ .

TL;DR: Formulae are derived for the number of cyclic binary strings of length n in which no single 1 occurs between two zeros and no single 0 occurs betweenTwo ones, by a problem of genetic information processing.

TL;DR: This chapter proposes a new combinatorial problem including a school timetable problem and gives some theoretical solutions to the problem, which seems very simple but general because it also includes a network flow problem, a graph-coloring problem, and some other combinatorsial problems as a special case of it.

TL;DR: Three or more probability distributions may be pairwise compatible but not collectively compatible, in the sense that they admit no common extensions, but pairwise compatibility proves to be a necessary and sufficient condition for collective compatibility when the underlying system of distribution schemes is “acyclic”.

TL;DR: It is established that three other edge-packing problems arising in reliability bounding are NP-complete, namely edge- packing by network cutsets, Steiner trees, and Steiner cutsets.

TL;DR: It is shown that G is virtually planar if and only if G is either planar or projective-planar and that sph( G ) = 1, 2 or ∞.

TL;DR: In this article, it was shown that a necessary and sufficient condition for the existence of a P 3 -factorization of K m,n is (i) m + n = 0 (mod 3), (ii) m ⊆ 2n, (iii) n ⩽ 2m and (iv) 3 mn/2(m + n ) is an integar.

TL;DR: This note proves that for odd m, m ⩾3, the edges of K m , m can be labeled with 1,2,3,4 in such a way that the (weighted) degrees of the vertices are all different.

TL;DR: This work has proved that if G is a digraph with n vertices and if each of these vertices has outdegree at least k, then G contains a cycle of length at most (n/k) +2500.

TL;DR: It is proved that h ( G) + 1 = l ( G ) + 1 and theorems of Chartrand and Wall and of Lesniak-Foster and Williamson are obtained.

TL;DR: A complete enumeration is carried out of self-complementary strongly regular graphs with fewer than 53 vertices for new necessary conditions for the cycles of complementing permutations and for the block valencies of the corresponding induced adjacency matrix partitions.

TL;DR: The number of spanning trees of G is bounded above by the number of degree sequence d1, d2,…, dn, where dn is the degree sequence of a graph.

TL;DR: This chapter discusses problems about the poset of subsets of a finite set, and gives problems for other families of posets.

TL;DR: It is shown how triad counts in multigraphs can be used in various kinds of statistical analyses of graphs and digraphs defined on a common vertex set.

TL;DR: An elementary proof is given for the number of convex polyominos of perimeter 2 m +4.

TL;DR: In the context of the combinatorial theory of ordinary differential equations recently introduced by the authors, a concrete interpretation is given to the classical method of separation of variables and this approach is extended and applied to systems of differential equations with forcing terms.

TL;DR: The chapter studies the relationships between toughness of a graph and the n-extendability of the graph and proves two results, essentially that if a graph has sufficiently high toughness (and has an even number of points) then it must be n-Extendable.