Showing papers in "Journal of Combinatorial Theory, Series B in 2000"

TL;DR: This work gives a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle that does not use the ellipsoid method or any other linear programming method.

TL;DR: “Crossing orientations,” the analogue of Kasteleyn's “admissible orientations” in this context, are introduced, describing how the Pfaffian of a signed adjacency matrix of a graph gives the sign of each perfect matching according to the number of edge-crossings in the matching.

TL;DR: It is shown that the covers in the skeleton of a category of finite relational models correspond naturally to certain instances of duality statements, and these covers are characterised.

TL;DR: In this article, it was shown that the determination of the pairwise crossing number and the odd-crossing number is an NP-hard problem and it is also NP-complete in the case of the crossing number.

TL;DR: Given a property P of graphs, write Pn for the set of graphs with vertex set n] having property P, where n is the number of vertices in the graph.

TL;DR: What appears to be a fundamental dichotomy of constraint graphs is investigated, by giving various characterizations of a class of graphs that is called dismantlable, by the space Hom(G, H) of homomorphisms from a locally finite graph G to a fixed finite constraint graph H.

TL;DR: There are exactly seven excluded minors for the class of GF (4)-representable matroids as mentioned in this paper, which is the smallest subset of GF matroid minors known to us.

TL;DR: It is proved that any set of 34 (n3)+cn2 triples from an n-set, where c is a suitable absolute constant, must contain a copy of the Fano configuration (the projective plane of order two).

TL;DR: New upper bounds on the spectral radius ?

TL;DR: It is proved that the number of non-isomorphic face 2-colourable triangulations of the complete graph Kn in an orientable surface is at least 2 n2/54?O(n) for n congruent to 7 or 19 modulo 36, and is at at least 22n2/81?O

TL;DR: A general result about homomorphisms of colored mixed graphs is proved which implies all earlier results about planar graphs and the notion of colored homomorphism for mixed graphs containing both colored arcs and colored edges is introduced.

TL;DR: It is proved that if e=u0v0 is an edge of G then the number of acyclic orientations having a unique source at u0 and unique sink at v0 is Crapo's beta invariant.

TL;DR: The study is introduced of a bialgebra of graphs, which is similar to the ring of graphs introduced by W. T. Tutte in 1946, and of the dual bial algebra of 4-invariants, which determines Vassiliev invariants of knots.

TL;DR: It is proved that with three exceptions, every tournament of order n contains each oriented path of order g, which is equivalent to n ≥1.

TL;DR: Several general inequalities for the G-indexed random walk are derived, including an upper bound on fluctuations implying that the distance d(f(u), f(v) is stochastically dominated by the distance to 0 of a simple random walk on Z having run for d(u, v) steps.

TL;DR: In 1971, Chartrand, Geller, and Hedetniemi conjecture that the edge set of a planar graph may be partitioned into two subsets, each of which induces an outerplanar graph, has nice generalizations for graphs embedded onto an arbitrary surface and graphs with no large clique-minor.

TL;DR: This work determines the minimum number of colors in an (H, q)-coloring of G, and proves the exact value of r, which is the smallest q for which r(Kn, n, K3, 3, 8) is linear in n and 2n/3⩽r

TL;DR: It is conjectured that almost all graphs are determined by their chromatic or Tutte polynomials and the evidence is provided to support this.

TL;DR: It is proved that K(n, k) is Hamiltonian for n?3k, and this is extended to the bipartite Kneser graphs.

TL;DR: A method for proving the optimality of an embedding is developed and examined and it is shown that metrics in the class (ii) are �(logn) far from the class l22, namely, the square of the metrics realizable in l2.

TL;DR: It is shown that, for all prime powers q, the set of excluded minors for GF ( q )-representability has at least 2 q −4 members and, for every field, F, the class of matroids representable over F is closed under segment–cosegment exchanges.

TL;DR: This work proves that for any given k there exists an f( k) such that any 3-connected graph on at least f(k) vertices possesses a contractible subgraph on k vertices, and considers restrictions to maximal planar graphs, Halin graphs, line graphs of 6-edge-connected graphs, 5- connected graphs of bounded degree, and AT-free graphs.

TL;DR: A decomposition formula for the zeta function of a group covering of a graph is given that decomposes as follows: zeta = 1, 2, 3, 4, 5, 6, 7.

TL;DR: A new connection between colorings and hamiltonian paths is presented and it is shown that if the chromatic polynomial of a graph has a noninteger root less than or equal to t0, then the graph has noHamiltonian path.

TL;DR: It is shown that any 4-connected graph that does not contain a minor isomorphic to the cube is aMinor of the line graph of Vn for some n?6 or a minor of one of five graphs.

TL;DR: This note establishes rk(C4)?k2+2 for k being an odd prime power for k?1 being a prime power.

TL;DR: A graph G is (n, ?)-connected if it satisfies the following conditions: (1) |V(G)|?n+1; (2) for any subset S?V( G) and any subset L?E(G) with ?|S|+|L|

TL;DR: The following finiteness theorem is proved: If Q is a well-founded quasi-order and k a fixed natural number, then there is a finite set ?

TL;DR: It is shown that conjectures of Thomassen (every 4-connected line graph is hamiltonian) and Fleischner (every cyclically 4- edge-connected cubic graph has either a 3-edge-coloring or a dominating cycle) are equivalent.

TL;DR: If n is sufficiently large and G=(V, E) is an n-vertex graph with ?(G)??n/2?, then there are edge-disjoint subgraphs of G which are isomorphic to H, and if h?1 divides |E| then there is an H-decomposition of G.