Anders Sune Pedersen

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A connected k-chromatic graph G is double-critical if for all edges uv of G the graph G − u − v is (k − 2)-colourable. The only known double-critical k-chromatic graph is the complete k-graph Kk. The conjecture that there are no other doublecritical graphs is a special case of a conjecture from 1966, due to Erdős and Lovász. The conjecture has been verified(More)
We consider the number of vertex independent sets i(G). In general, the problem of determining the value of i(G) is NP -complete. We present several upper and lower bounds for i(G) in terms of order, size or independence number. We obtain improved bounds for i(G) on restricted graph classes such as the bipartite graphs, unicyclic graphs, regular graphs and(More)
A connected k-chromatic graph G is said to be double-critical if for all edges uv of G the graph G− u− v is (k− 2)-colourable. A longstanding conjecture of Erdős and Lovász states that the complete graphs are the only double-critical graphs. Kawarabayashi, Pedersen and Toft [Electron. J. Combin., 17(1): Research Paper 87, 2010] proved that every(More)
Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233–237] proved that every connected subcubic triangle-free graph G has an independent set of order at least (4n(G) − m(G) − 1)/7 where n(G) and m(G) denote the order and size of G, respectively. We conjecture that(More)
An inflation of a graphG is obtained by replacing vertices inG by disjoint cliques and adding all possible edges between any pair of cliques corresponding to adjacent vertices in G. We prove that the chromatic number of an arbitrary inflation F of the Petersen graph is equal to the chromatic number of some inflated 5-cycle contained in F . As a corollary,(More)
The Conjecture of Hadwiger implies that the Hadwiger number h times the independence number α of a graph is at least the number of vertices n of the graph. In 1982 Duchet and Meyniel proved a weak version of the inequality, replacing the independence number α by 2α− 1, that is, (2α− 1) · h ≥ n. In 2005 Kawarabayashi, Plummer and the second author published(More)
We prove several best-possible lower bounds in terms of the order and the average degree for the independence number of graphs which are connected and/or satisfy some odd girth condition. Our main result is the extension of a lower bound for the independence number of triangle-free graphs of maximum degree at most 3 due to Heckman and Thomas [A New Proof of(More)
A circulant is a Cayley graph over a cyclic group. A well-covered graph is a graph in which all maximal stable sets are of the same size α = α(G), or in other words, they are all maximum. A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. It is not difficult to show that a circulant G is a CIS graph if and only if G(More)