50,358 research outputs found
Balancedness of subclasses of circular-arc graphs
A graph is balanced if its clique-vertex incidence matrix contains no square submatrix of odd order with exactly two ones per row and per column. There is a characterization of balanced graphs by forbidden induced subgraphs, but no characterization by mininal forbidden induced subgraphs is known, not even for the case of circular-arc graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. In this work, we characterize when a given graph G is balanced in terms of minimal forbidden induced subgraphs, by restricting the analysis to the case where G belongs to certain classes of circular-arc graphs, including Helly circular-arc graphs, claw-free circular-arc graphs, and gem-free circular-arc graphs. In the case of gem-free circular-arc graphs, analogous characterizations are derived for two superclasses of balanced graphs: clique-perfect graphs and coordinated graphs.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Chile; ChileFil: Safe, Martin Dario. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Wagler, Annegret Katrin. Centre National de la Recherche Scientifique; Franci
On hereditary graph classes defined by forbidding Truemper configurations: recognition and combinatorial optimization algorithms, and χ-boundedness results
Truemper configurations are four types of graphs that helped us understand the structure of several well-known hereditary graph classes. The most famous examples are perhaps the class of perfect graphs and the class of even-hole-free graphs: for both of them, some Truemper configurations are excluded (as induced subgraphs), and this fact appeared to be useful, and played some role in the proof of the known decomposition theorems for these classes.
The main goal of this thesis is to contribute to the systematic exploration of hereditary graph classes defined by forbidding Truemper configurations. We study many of these classes, and we investigate their structure by applying the decomposition method. We then use our structural results to analyze the complexity of the maximum clique, maximum stable set and optimal coloring problems restricted to these classes. Finally, we provide polynomial-time recognition algorithms for all of these classes, and we obtain χ-boundedness results
On the Complexity of Spill Everywhere under SSA Form
Compilation for embedded processors can be either aggressive (time consuming
cross-compilation) or just in time (embedded and usually dynamic). The
heuristics used in dynamic compilation are highly constrained by limited
resources, time and memory in particular. Recent results on the SSA form open
promising directions for the design of new register allocation heuristics for
embedded systems and especially for embedded compilation. In particular,
heuristics based on tree scan with two separated phases -- one for spilling,
then one for coloring/coalescing -- seem good candidates for designing
memory-friendly, fast, and competitive register allocators. Still, also because
of the side effect on power consumption, the minimization of loads and stores
overhead (spilling problem) is an important issue. This paper provides an
exhaustive study of the complexity of the ``spill everywhere'' problem in the
context of the SSA form. Unfortunately, conversely to our initial hopes, many
of the questions we raised lead to NP-completeness results. We identify some
polynomial cases but that are impractical in JIT context. Nevertheless, they
can give hints to simplify formulations for the design of aggressive
allocators.Comment: 10 page
Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes
A hole in a graph is an induced subgraph which is a cycle of length at least
four. We prove that for every positive integer k, every triangle-free graph
with sufficiently large chromatic number contains holes of k consecutive
lengths
Induced subgraphs of graphs with large chromatic number. II. Three steps towards Gyarfas' conjectures
Gyarfas conjectured in 1985 that for all , , every graph with no clique
of size more than and no odd hole of length more than has chromatic
number bounded by a function of and . We prove three weaker statements:
(1) Every triangle-free graph with sufficiently large chromatic number has an
odd hole of length different from five; (2) For all , every triangle-free
graph with sufficiently large chromatic number contains either a 5-hole or an
odd hole of length more than ; (3) For all , , every graph with no
clique of size more than and sufficiently large chromatic number contains
either a 5-hole or a hole of length more than
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